I have a BS in Computer Engineering and a MS in Biomedical Engineering. I recommend getting a MS if you are interested in biomedical research. Depending on the program, you might not have time to take the premed classes with your engineering classes, especially if you are doing a thesis. I recommend doing a thesis because it demonstrates your ability to do independent research, plus as a research assistant your tuition is paid with a stipend (in my case). If you do plan on taking premed classes, make sure your advisor or program is supportive, because you need their letter of recommendation. It was too late for me to take my premed classes during grad school, so I worked as a Healthcare IT consultant for a year and I recently got into the Scripps post bac program, I think it's worth the investment. Good luck!