Medical schools take students from all different backgrounds; in fact I think that many medical schools encourage studies outside of the traditional sciences of biology/chemistry/biochem. Don't forget, however, that you would still have to take the required premed classes as well as the MCAT.
The bigger question is what career would you prefer- being a physician and working with people or doing research? I suggest shadowing a physician for a few times to see what it really is like (people often have misconceptions about what being a physician is really like). If being a physician is truly your dream and your shadowing experiences confirm that, then why not "embrace your dream?"
Something that you might be particularly interested in are combined MD/PhD programs. These programs are often NIH funded programs through select medical schools and allow/require you to do your first two years (classroom years) of medical school, then work on research for a PhD for usually 3-4 years, and finally complete medical school (the last two years/hospital years). You are awarded an MD and a PhD at graduation. These programs are generally geared towards people who want to do health-related research in addition to practicing as a physician. The government funds these programs, so your tuition is usually paid for and you receive a monthly stipend with the general agreement that you teach and do research as part of your career. Good option if it is something that interests you. To find out more, check-out
http://services.aamc.org/currdir/section3/degree2.cfm and select the PhD degree that interests you.
Best of luck!