In an earlier thread, (if I got this right) it looked like you were intending to also apply to Ohio State as an in-state student. Did this happen? Were you accepted? If so, then what would it cost?
I agree with @dimkin that most students who start university as premed end up changing their mind. However, it would seem unfortunate to attend a university where the cost of the university is going to make medical school unlikely even before you show up for the first week of classes as an undergraduate student. Also, running up excessive debt can be a problem even for students who have a major that leads to a solid career with a bachelor’s degree.
And I do think @David_D you are correct to be aware of “Caltech’s rigor”. I had experience at a similarly rigorous university (MIT) and it is something to think about. You need to want to do it. I do not think that Cornell is much different in this regard.