I asked two doctors I know where the other students in their MD program had gotten their bachelor’s degrees. One said “all over the place”. The other said essentially the same thing (but not with quite as memorable of a quote).
I do not have any MDs in my immediate family. I do have multiple close relatives who either have or are currently getting a graduate degree in a biomedical field (master’s degrees, DVM, or PhD, plus a family friend who is a PA). Some are currently involved in patient care (whether human patients or non-human patients). One is currently involved in biomedical research. All of them have said essentially the same thing. Graduate students in biomedical programs come from a very wide range of undergraduate universities.
The University of South Carolina, U. of Maryland, and Texas A&M are all very good universities. All will prepare you well for applying to MD programs.
The vast majority of students who start university thinking “premed” end up doing something else. Some cannot maintain a medical-school-worthy GPA in very tough premed classes. Some just decide that they want to do something else. There are a lot of forms of “something else” to choose from, some of which are biomedical-related and some of which are not. The three universities that you mentioned all are very good for many forms of “something else”.
Medical school is insanely expensive. You should be making an effort to save as much as you can while getting your bachelor’s degree. It would be best if you can keep some $$$ in the college fund for graduate school. Of course this is not always possible for every student.
I do not know what state you are from. However, I think that you should also apply to your in-state public university or universities.
Then wait and see what sort of offers you get, and see what each school will cost you before you decide where to attend.
And if medical school is a realistic option, then you and your parents should be budgeting for a full 8 years of university.