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So that's an excellent question, firstly majoring in pre-med is an excellent start. However, you should not feel like that is what you MUST do in order to get into medical school. My best advice would be to look at the individual medical schools that you are interested in and take a look at what requirements they each have. For the most part admissions committees look first at GPA and MCAT, after that they are interested in you as a person and what inspired you to pursue a career as a physician, what sorts of volunteer and leadership activities you have been involved in. Transferring schools should have no impact.