Brown’s website states that its COA annually is currently estimated to be $80,448, a number which will surely go up in coming years. That’s over $320,000 in cash.
On the other hand, your expenses at OSU would be minimal, if “full ride” covers tuition/room&board/books/fees-does it?
Brown is an amazing school, but if you have a “full” full-ride, think of all the things that you could do with $320,000+.
And medical school is almost unbelievably expensive, and there are virtually no scholarships/grants; it’s full pay for almost everybody. And if you do go to medical school, the first several years(can be many years, depending on specialty) you’ll be making a nominal salary.
The name of your UG will not get you into medical school; that will be up to you. You clearly have a proven academic track record; apply that to your studies at OSU and save your money.