Taking care of a relative is very stressful especially when theyare very sick. You are right that this could be a difficult time. But don't wait for he to apologize. She may see you as hurtful and insensitive. So by all means call and sort this out. People act very erratic when they are under stress especially when facing too many responsbilities. Try to verbalize your position however so she knows that this was about her not keeping her word. If she is willing to listen, she will see things from your perspective too. She may at that time felt that you had caused her more stress when she was already stretched too thin.
If she is done, you will have to accept that. But she very likely felt unsupported as well. The only way to know is to make that call. There is always a chance that someone wants to end a relationship but you won't know that if you don't swallow our pride. Try to call, talk a lot, find a compromise, and go from there.