Math is not my strongest subject however just the very theory is extremely interesting to me.
So it's easy to interpret this in many ways, but just know that any engineering major, including BME, is very, very heavy on math. Problem sets, labs, lab reports, Matlab, modeling, projects, and exams. On the exams for instance, you have to be accurate with your math (duh) and
fast enough to get all the questions done before time's up.
In many courses the test average could be in the 30s -- like seriously "failing" -- before any curve to bump everyone's grades up. It varies considerably. But please know what you're getting into.
Engineering is its own end-goal career path and discipline, so there may be different standards of evaluation. I was Computer Engineering (similar to Electrical Engr and CompSci) before I was BME, and I remember the departmental advisor/professor was letting prospective majors know, "You'll totally be successful and get a great job with even a 3.0 GPA. 2.9? Not horrible. 3.1? 3.2? 3.3? Excellent GPAs." The bar is calibrated differently since many schools don't necessarily curve or have grade inflation to boost the overall class average.
It could be perilous if medical school is a concrete goal of yours. The math is frequently similar to physics problem sets but with different concepts. Nerve signalling and integration. Applying sensors to cell membranes. Like stuff you learn in cell bio, biochem, and physiology but throw in physics and calculus and algorithms and models, and there's your BME problem set or exam. You must be accurate and fast with math (bears repeating!).
BME is a big field with many sub-specialties. It's been years so things like imaging/computing tract (how MRI/CT/imaging works and how to make it better), tissue engineering, cardiac bioelectricity, prostheses/mechanics, medical devices and instrumentation, nerve conductivity and I'm forgetting a bunch.
Protein engineering/synthesis seems, to me, to be more on the cellular/genomics/molecular bio side and much closer to traditional bio, chem, and biochem, but more cutting edge of course. Computational biology and computational chemistry, maybe bioinformatics.
Maybe get your feet wet in BME or engineering in general (if there's an "Intro to BME" course you can take) before diving in? You may be able to still learn BME/nerdy/techy/biophysic-y concepts without having to major in the field and better preserve the GPA. I'm not saying that 3.7 or higher are impossible, but they're... much more rare and require more sacrifice. Since the engineering standard is already calibrated much lower with the expectations that graduates go on to industry or graduate school.
Something to think about. Oh, did I mention, you must really love doing tons of math and problem sets and physics and algorithms? There's definitely cool factor but also pucker factor. Brace yourselves. Winter is coming (for your GPA).
😉
Edit: Maybe another way you can get the best of both worlds is -- if it's offered -- do a BME minor, so you get a good foundational introduction to the field and can take a few electives you find interesting but don't need 3-4 years of hardcore engineering courses on top of the usual BCPM pre-reqs. So neuroscience major (or whatever), BME minor?