Take all this "I love bme" with a grain of salt.
First of all, the job opportunities are NOT that great. Sure, more companies that apply engineering to medicine are popping up, but they want more specialized engineers such a chemical, electrical, or mechanical with biology knowledge. A jack of all trades BME is not always desirable, and some people actually have very a difficult time finding a job. If you really want a fall back if medicine doesn't work out, then go into a different engineering.
As for your passion for math and physics, you actually wont learn as much of these things as you probably want. You learn alittle bit of math, alittle bit of physics, some circuits, some chemical engineering, some mechanical. The problem is you learn nothing in depth. Atleast for me, I've been left wanting more.
As for medical school, all this "thinking critically helping you on the MCAT" is bull****. What helps you on the MCAT is your MCAT prep, not your major. Your GPA is likely to drop unless you spend too much time studying like me, and adcoms don't give 2 ****s about what major you are, so it can be a detrimental major in that regard. And the "study habits" for engineering are completely different than the ones applied to med school like classes (like biochem). One is HEAVY math based, involving many many practice problems. The other is memorization, no math. I honestly study completely different for my premed and my engineering classes. If you want a major that will prepare you well for medical school, do biochemistry.
This is just my own personal experience, but my BME professors have mostly been absolutely ****ing terrible. Like worst professors ever. Disorganized class, stupid meaningless material, and lectures. If you're going to a high ranked BME program, maybe you'll have a better experience.
Imo, many majors are just plain superior to BME. If I could do it all again, I would be a biophysics major and do some actual science.