Hi Etije- Within BME, you have a large variety of concentrations to pursue, many of which have a basis in other core science fields. A few examples for you: Imaging is a big focus within BME and could involve lasers, different wave emissions (MRI, ultrasound), and optics among others, so you would benefit with a good foundation of physics. Tissue engineering is another big focus- growing different types of cells in a dish or on a scaffold to make new body parts or make a functioning version to screen drugs, test diseases, or apply stress. This would be a great option for those who are cell biologists at heart. Fabrication and design of prosthetic limbs lends strongly to mechanical engineering and possibly electronics. There's a whole lot of cross talk between all of these fields and this is just the tip of the iceberg, so there's room for wherever your enthusiasm and interest lies.
The great thing about BME is that you will gain a broad appreciation for all of these things if you major in it as an undergrad. Programs are likely to have different strengths based on the specialties of their faculty. Some of the challenges recent grads are facing has to do with that same broadness of the field, requiring an advanced degree to specialize in whichever field of BME most interests you. If you have a strong pull to a specific field within BME from what you've been exposed to already, I would suggest considering what the associated field is as a potential primary major to build that core foundation (physics, mechanical engineering, etc). Options might be available to choose it as a double major if that fits your plan.
Regardless of your major, it would be great experience to become involved with a research lab as an undergraduate- see what project and settings get you most excited. Some colleges offer summer lab opportunities for high school students, too, that might give you a good experience and help recognize your passion.
Long winded answer for you- I hope that was helpful. Best of luck, Etije!