My mother has a heart problem so taking care of her was the only thing I could do all of my high school.My father and brother live out of town so does this harm my profile??
No.
But it will help your application if somebody else refers to it in their LoR. For example, your GC “I know that @UIUCbound was sorry that s/he couldn’t participate in X EC, b/c of the home-care responsibilities” or a teacher “I was always impressed that @UIUCbound could deliver this quality of work, given all of the home care responsibilities s/he had”.
And, you can talk about what you did do in your non-schoolwork time (which you should have had some of, even with caring for your mother).
Also, as an international student you aren’t expected to have US level of ECs