First off please don't do the internship because you think it will look cool. There are tons of people who would love to have that analyst spot to help establish their future careers, and you would be taking it just to do something cool. In addition, you are wasting the company's time. Company's use these summer analyst jobs to find new employees and by you taking the job you are being extremely disrespectful and inconsiderate. If you are serious about wanting to do I-banking why don't you apply for summer analyst and if you are even able to get a position, take it with the intention of accepting if you get a full-time offer. Most offers you will get will only be 2-3 years, this will allow you to work in the field, see if you like it (who knows you might realize that it is your true calling), if not at least you will have a decent amount of money to help you out through med school and offset a lot of debt. If you are already accepted to a school I am sure if you explain to them your situation they would not mind you taking two years before starting. Or if you haven't applied and are serious about finance, your MCAT score is good for three years and you will stand out among all of the other applicants having come from this background now to med school.
I guess what I am trying to say is please do not waste everyones time and resources just to do something that would look cool. It is extremely rude, inconsiderate, and disrespectful. Not to mention I am sure adcoms will not be too fond of it either, it shows that you are willing to waste other peoples time for your own personal benefit and experience.