Despite the day of her re-diagnoses being the vilest days of my life
rubbing my sister's back and consoling her as she retched over buckets
However, if I can one day look at a child and know that he or she is able to live the full life they deserve because of my devotion, I will feel just as glorified.
This is very powerful, and well-written too. The only thing I would comment on is that by talking about how difficult your sister's cancer made your life, you kind of downplay the pain
she must have been going through. Maybe if you write less about the negative effects the cancer had on your life or spent less time intro-ing with the heroes, you could talk more about the effect seeing her sick had on you, which would drive your compassion for children with cancer home more and make it seem less like becoming a doctor is your duty as a person who survived adversity.
Also, your "life is precious" theme doesn't really play out in:
It was this insight that enabled me to endure faking my happiness in high school while watching my grades dwindle under stress, rubbing my sister's back and consoling her as she wretched over buckets, and having to forfeit a year of my youth when we moved countries to receive specialized, more intense treatment.
That quote makes me think more of enjoying the little things in life; taking comfort in the fact that even when life sucks, things can get better; no matter how bad your life seems, be grateful because others have had it worse, etc.