BME is a fools gold major. Most graduates have trouble finding jobs in biotech, aren't refined and educated enough to get jobs in other fields of engineering, and have been ramrodded by their difficult course load and their GPA ends up taking a hit. There are, of course, few exceptions to this.
If you want to be an engineer, do mechanical, civil, electrical,etc and just take up the med pre reqs. Be advised it will be hard but you will have a "backup" if you don't get accepted into medical school.
If u really wanna just wanna be a physician, go ALL IN. Cut the engineering stuff and strictly pursue medicine by picking a major that won't be as tolling as engineering. You will have a fire under ur a$$ knowing there is really no "career" to fall back on.