Biomedical engineers are all over the healthcare industry! I have friends who are working on things like prosthetic limbs to disease delivery. Its a very diverse and flexible major with many avenues for employment. One word of warning is that it is a very tough degree because you have to learn many different subjects with lots of tough classes. Not only do you have to learn biology and chemistry, you even have to take programming classes and circuits at my University since they want you to have the ability to work with robotics.
Another thing is that these healthcare companies are typically looking for focused experts like grad students and PHD students because they need that expertise for the things they work on. You'll find many jobs restricted to really focused disciplines. Doesn't mean there aren't opportunities for undergrads, its just that the better jobs need more schooling.
Glad you want to be an engineer! We definitely need more. Good luck!