Congenital heart disease.

https://www.marchofdimes.org/baby/congenital-heart-defects.aspx

Congenital means present at birth. Congenital heart defects are heart
conditions that a baby’s born with. These conditions can affect the
heart’s shape or how it works, or both.

Congenital heart defects are the most common types of birth defects.
Birth defects are health conditions that a baby’s born with that
change the shape or function of one or more parts of the body. They
can cause problems in overall health, how the body develops, or in how
the body works.

Congenital heart disease lends itself to a story because the children are cognitively normal, not contagious, not doomed like someone with cancer but limited for cardiopulmonary reasons. They can be maintained with surgery and medical care but many die young - in childhood or young adulthood. Some can be cured with a heart transplant but even if that is a possibility for your character, transplant recipients still have issues and of course can also have issues from the immunosuppression required to keep the transplant.

If you leave it at that - girl tends to be blue, out of breath, sickly, born that way - that would suffice for a story. If you need to get into the weeds read more on Tetrology of Fallot. It is one of several congenital cardiac syndromes that could work for you.

Cystic fibrosis

Despite the name, the problem there is you produce much thicker body fluids than normal. The largest problem is mucus, which can coat the linings of the lungs, thus causing problems like lung infections, which often require long hospital stays to fix. It's often caught in infanthood, but there's no way to treat the underlying problem, so you treat the symptoms. Some cases do manifest outwardly (and subtly), but many do not.

As to it being an inheritable trait, it's quite possible that she got unlucky in the gene pool

Every person has two copies of the cystic fibrosis transmembrane conductance regulator (CFTR) gene. A person must inherit two copies of the CFTR gene that contain mutations -- one copy from each parent -- to have cystic fibrosis.

Her sisters are healthy because they got one good gene (they are still carriers of the bad one, though).

This fits your story well, because she could seem to be holding up fairly well, and then abruptly take a turn for the worse and die from a lung infection.

Juvenile Tay–Sachs disease

While the more common infantile form is typically lethal before the age of 4, the much rarer juvenile version will see your unfortunate girl dead anywhere between ages 5 and 15. This disease is caused by a mutation that prevents cells from breaking down a certain waste molecule. This molecule continues to build up inside cells over a period of years until it reaches toxic levels and begins killing neurons. Like the more common infantile form, it is invariably fatal.

It must begin having an effect on her from a very young age.

The onset typically occurs between ages 2 and 6.

Is terminal and can kill her by her early teens (14 years old at the latest) even with access to the best medical resources. Not that people can't live beyond that age, but that medical resources can't guarantee a prolonged life.

She will likely die a preteen or young teenager, depending on how severe the case is. Treatment is entirely supportive, easing the symptoms (cognitive and motor skill deterioration, dysarthria, dysphagia, ataxia, and spasticity) but incapable of prolonging life.

It is NOT cancer.

Juvenile Tay–Sachs disease is a mutation in the beta-hexosaminidase A enzyme. This enzyme typically breaks down a waste molecule called GM2 ganglioside. As people afflicted with this disorder are incapable of breaking down this ganglioside, it builds up to toxic levels in cells over a period of years.

Would leave her in the hospital frequently and for prolonged (business week-length minimum) stays.

As treatment is supportive, frequent hospital visits are likely.

Is NOT a dominant-allele genetic disorder. (If genetic, it needs to be recessive or not guaranteed to affect a person who has it. She has multiple sisters who should be healthy is why.)

The disease is inherited in an autosomal recessive manner. It is a mutation on the HEXA gene on chromosome 15. Note that it is possible for a dominant-allele to appear spontaneously in someone with no family history of the disease due to random mutations. It would not be impossible to have a fatal illness caused by a dominant mutation while having perfectly healthy sisters.

Does not result in any visible outward deformities.

The disease primarily affects the nervous system.

You could go with a variant of the Rett Complex syndromes. It is a rare (1:10000) genetic condition which is usually acquired "de novo" (i.e. with both parents healthy), only fully understood twenty years ago, which mainly affects females (males die shortly after birth except in rare cases).

This link describes the most common and severe forms of RCS.

Some milder forms allow normal development up to a certain age (6-10 years), but have secondary cardiac involvement. As a result, the victim may experience fainting and/or seizures (which would lead to her condition being discovered), or sudden death due to cardiac arrest (triggered by physical effort, emotional stress, or idiopathic). The heart itself is healthy, so transplant is not an option.

Due to the variability of the disease, it could be plausible for a victim to show few symptoms (hand wringing, slight unsteadiness when walking, mild speech impairment, restlessness) and need nothing else except for a non-periodical SSRI course (anywhere up to two weeks' hospitalization and home follow-up).

Symptoms are progressive, and a mild form might look to a life expectancy in the forties; there would be no reason to be certain of death before age 14 (unless the form was more severe, but in that case you'd be looking at heavier development anomalies - microcephaly, etc.).

On a historical note, tuberculosis used to kill a broad range of ages, and can take years to kill. In this case, you need only specify that this is a new strain, and one which is resistant to all current antibiotics. Which is not at all a far-fetched assertion, since strains exist which are, in fact, resistant to the major antibiotics. Google on "drug resistant tuberculosis".

Depression

With the onset of puberty, she goes into a deep depression and starts to cut herself, and eventually succeeds in her own suicide.

1. Puberty can start as early as 7 years, but most commonly around 11 for girls.


2. Suicide is fatal, so if the depression causes it, then this is satisfied.


3. Non-Cancer


4. Attempted suicide will leave her hospitalized, and include time for psychiatric help.


5. Depression can have a genetic component, but not always. So this is fine.


6. As long as you don't count dark makeup and scars from self cutting, there are no physical deformities.

Kidney failure

This could be from ingesting some toxic substance, or through some developmental abnormality. There are inherited conditions which would cause this as well, but there are plenty of other possibilities.

Dialysis is required for any kind of medium-term survival. However it does not work forever. Eventually toxins will build up to damaging levels, and the patient dies. Or the patient develops sepsis or some other hospital-related bug and dies.

A kidney transplant will solve the problem. However there are many more patients needing transplants than there are matched donor organs. Sadly, many patients do die whilst waiting for a suitable donor organ.

She got AIDS from her mother during her gestation. Her mother got infected after giving birth to her older sister, so the sister is not infected. Or alternatively she could have got it via a transfusion in very young age.

Current medications of AIDS can improve life expectation, symptoms start showing from early period, however there is no cure yet.

One way to satisfy a lot of these conditions (especially #5) is to consider a condition that develops as a result of an injury. An injury doesn't have to leave any significant external marks, but can result in irreparable and critical damage to vital organs. This might have been caused by blunt force trauma, or being exposed to the shockwave of an explosion. Injuries can happen at any point in life, and are easy to apply to only the target character.

You can tweak the details to fit whatever story elements you wish to have. As one example, extensive damage to the renal system will impact the body's ability to filter out toxins and can require treatments like dialysis to compensate. If the kidneys' functionality is intermittent or inconsistent, you can have sudden and unpredictable build-ups of toxins that themselves can cause side-effects requiring hospitalization. Dialysis may extend life for an unpredictable period of time but won't fix the problem. The patient needs a transplant but due to her injuries, she wouldn't survive transplant surgery (perhaps due to heart damage). Instead, her choice was to continue dialysis treatments and buy as much time as she can. Perhaps the rapid hormonal changes that occur during the onset of puberty exacerbate the problem and accelerate the body's decline. You can come up with your own details of course, since injuries don't necessarily have well-defined sets of symptoms or side-effects.

Some Guy's Syndrome

Some Guy's Syndrome, named after that famous guy, you know, that one, who got the disease and raised awareness some time ago. Some Guy's Syndrome is part of the great family of Plot Diseases, that covers a wide variety of illnesses, ranging from harmless to lethal.

The effects of Some Guy's Syndrome are <insert plot-dictated effects here>. It is <viral/bacterial/genetic/magic> in nature, and is <somewhat/very/extremely/not at all> serious indeed.

In other words, describe the effects you want, slap a name on it, and voilà. Unless there is a reason you want a real disease armchair doctors will tell you doesn't work the way you want.

Duchenne Muscular Dystrophy (DMD)

Unfortunately, this is a real thing. No magic, no sci-fi, no cure. It looks like it checks all the boxes, which is to say that it starts early, kills young, and overall sucks. It was the first thing that came to mind, although I could be biased by personal experiences.

1. It must begin having an effect on her from a very young age.

Muscle weakness can begin as early as age 3, first affecting the muscles of the hips, pelvic area, thighs and shoulders, and later the skeletal (voluntary) muscles in the arms, legs and trunk. The calves often are enlarged. By the early teens, the heart and respiratory muscles also are affected.

2. Is terminal and can kill her by her early teens (14 years old at the latest) even with access to the best medical resources.

Thanks to advances in cardiac and respiratory care, life expectancy is increasing and many young adults with DMD attend college, have careers, get married and have children. Survival into the early 30s is becoming more common, and there are cases of men living into their 40s and 50s.

That is, even the best, latest medicine can only hope to make it longer. The average life expectancy is 26. As seen above, by the early teenage years your cardiopulmonary system is already compromised, and it kills in the early teenage years often enough.

3. It is NOT cancer.

It is not.

4. Would leave her in the hospital frequently and for prolonged (business week-length minimum) stays.

Depends mainly on the state of progression. If the lungs are severely compromised, assisted breathing is common. There's a higher than average risk of cardiomyopathy, which may necessitate surgery, etc.

5. Is NOT a dominant-allele genetic disorder. (If genetic, it needs to be recessive or not guaranteed to affect a person who has it. She has multiple older sisters who should be healthy is why.)

DMD carriers are females who have a normal dystrophin gene on one X chromosome and an abnormal dystrophin gene on the other X chromosome. Most carriers of DMD do not themselves have signs and symptoms of the disease, but a minority do.

It's rare, but possible, for a female to be affected by DMD, rather than just being a carrier. You say she has healthy sisters, so this fits perfectly with that. It would mean they are likely carriers (and should probably get tested to know for sure). Indeed, it especially fits because it's unexpected in females.

6. Does not result in any visible outward deformities.

The main visible side effects are enlarged calves and curvature of the spine. They don't happen in all cases, though, and usually not until the later stages.

7. I'd like for her to at least be able to walk and run on her own to some degree, but this isn't inherently a necessity. That said, she can be limited by her malady. Otherwise, the more bedridden she is, the better to help nail in the point that she is sick even if she tries not to show it.

Sooner or later, a wheelchair is needed in DMD, typically by about age 12. Unless there's an injury, such as a broken leg, wheelchair use usually is gradual. Many at first use wheelchairs for long distances, such as at school or the mall, and continue to walk at home.

Braces, standing frames, and wheelchairs are commonly used, but until the end stages, walking is encouraged because regular exercise helps keep the symptoms from progressing as quickly.

The quoted information came from the Muscular Dystrophy Association, and associated links from that page.

Progeria could potentially work for you, although I realise the main downfall with this is that it has some outward/visible manifestations (stunted growth, alopecia, and a distinctive head shape). Having said that, it seems to tick your other boxes:

Progeria is ‘premature aging’ - basically, it causes you to age at about eight times the rate of a normal human. Some people with progeria can live into their twenties, but most live only to late childhood/early teens. Wikipedia says “as there is no known cure, few people with progeria exceed 13 years of age”, which fits with the age you’re looking at for your character.

It also doesn’t necessarily affect siblings - there are some very rare cases where siblings have progeria, but it generally develops during cell division in one of the parents’ gametes, or in the newly-conceived zygote, and thus won’t impact other births.

Progeria is not cancer - and even though it can make it more likely that sufferers contract certain age-related conditions, it does not have a correlation with greater risk of cancer. (Things that are more likely include: atherosclerosis, loss of eyesight, wrinkled skin, kidney failure, and cardiovascular problems).

With all the inherent complications of the disorder, people with progeria can need to spend a lot of time in hospital. Progeria isn’t necessarily immediately noticeable, but becomes more impactful as times goes on - and would certainly be likely to have an effect by the age of 9 (and more likely by 18-24 months). However, this frequent hospitalisation wouldn’t necessarily mitigate activity - children with progeria can still be active. This may need to be less rough than for children without progeria, but swimming, walking around, bowling, etc. are certainly possible for those with progeria. The other thing with progeria is that those with the disorder do not suffer from any mental development deficiencies - on the whole, they are reported to have average to above-average intelligence, and thus can definitely take part in things on a level with those their own age, even if playing rugby might not be the most sensible option.

Haemophilia may work. I think it hits all your points, however, I am not able to confirm if it fits 5 (although I think it does).

Death could occur at puberty with the onset of menstruation.

Polio comes to mind.

I am pretty sure about points 1, 3, 4, 5

Regarding point 2: People can survive Polio, yet I guess this depends on the available treatment.

Regarding point 6: while deformations have been observed, complications vary for individuals

1. It must begin having an effect on her from a very young age.


2. Is terminal and can kill her by her early teens (14 years old at the
   latest) even with access to the best medical resources. Not that
   people can't live beyond that age, but that medical resources can't
   guarantee a prolonged life.


3. It is NOT cancer.


4. Would leave her in the
   hospital frequently and for prolonged (business week-length minimum)
   stays.


5. Is NOT a dominant-allele genetic disorder. (If genetic, it
   needs to be recessive or not guaranteed to affect a person who has it.
   She has multiple sisters who should be healthy is why.)


6. Does not result in any visible outward deformities.

Although not part of the required points, the original poster wants to avoid name-dropping the disease.

A teen girl that suffers through phases of lethargy or even paralysis, is a strong indication of Polio, although I grant that in the modern western world many people might be too young to immedeately think of Polio, since this disease has been successfully eradicated.

A real-world disease that almost meeds your requirements is Sickle-cell anaemia. https://en.wikipedia.org/wiki/Sickle_cell_disease

Average life expectancy for an affected female in the Western world is around 45, but lower if advanced medical care is not available. The disease causes a series of crises throughout life, any of which could prove fatal. It's caused by inheriting a recessive gene from both parents.

It's rare for it to cause death before adulthood. It was not eliminated by evolution because inheriting the gene as a single copy conveys resistance to Malaria, and this advantage to the many outweighs the disadvantage to relatively few.

You might tweak this disease into something fictional, or simply make your character exceptionally unlucky (if she has access to modern medicine, at least). Some research might uncover a combination of this with some other normally minor condition that together create an even worse prognosis. (The common other minor condition, is ageing).