There is no pre-med major persay, being premed is pretty much just going through your undergrad with the intent of going to medical school. So when you say it's not accredited idk what you mean because BME is accredited at UCI. As far as I know the minimum requirements of getting into medical school are an undergrad degree and an mcat score. Everything else varies from person to person. As BME I'm sure you will have ample opportunity to take classes that will help you on the MCAT or get you into research. Medical schools often have a list of recommended classes like anatomy, but they are not rigid requirements. Also, as BME there will likely be lots of overlap with the other general bio sci premeds, especially if u have to do the bio core.