The OP mentions “health care reasons.” In my experience and that of others I know (anecdotally), having medical problems while accomplishing at the level the OP has accomplished, is a big plus for admission. Ability to overcome challenges, resilience, grit and so on. On top of homelessness, caring for sister etc.
I didn’t jump to the conclusion that the OP has mental health issues, but I would say those are not always a negative unless the essay and interview make it clear that those issues continue in a way that would deter success.
Again, the OP has only mentioned health issues, not mental health issues, so I don’t think this tangent is even necessary. As another poster wrote, the OP has a great story.