EEundergrad

Hey guys, I'm currently a junior EE major in college. All this time, I have also been pursuing pre-med classes because I wanted to go to medical school. However, lately, I am thinking that graduate school is better suited to me. I have been doing research since freshman year and have kept a 4.0 GPA since I thought I would be applying to medical school. My question is this: the research I have been doing has been in a chemistry lab working with nanotechnology, almost completely unrelated to EE - how much will this hinder my application? In particular, I am looking to apply to MIT and Stanford's EE program. Will I be a competitive applicant based on 3 years of unrelated research and a 4.0? I was also a Goldwater nomineee from my undergraduate institution and am still awaiting the final results of the competition. Would it be wise to apply to both Grad school and Medical school and then decide based on where I get in? I have already finished all my pre-medical pre-reqs and have taken the MCAT so I'm all set for medical school. Any feedback is appreciated. Sorry for the long post and thanks in advance.