You can’t major in “medicine” as an undergrad. You can major in psychology and the also take the required courses for medical school applicants. You can do that at just about every four year college in this country. Why BU? You might get accepted and you might not. Admissions have become more competitive in recent years. So when the time comes, apply and see.
Your parents and you can run the net price calculators for all of these colleges to see what the possible net costs will be…and whether they are affordable.