Should I major in electrical or mechanical engineering?

I am currently a freshman, and I came into college pretty sure I was going to major in either Bioengineering or Biomechanical Engineering, since I really want to become a biomedical engineer (I really like medicine/biology, but I also really like math and physics). However, after speaking to faculty/students/alumni, it seems to me that these majors are a bit broad with not necessarily enough depth in one area, and majoring in a fundamental engineering discipline first might be a better idea. As a result, I’m trying to decide whether to major in Mechanical Engineering and maybe take some bio classes on the side or in Electrical Engineering with some depth classes in bioelectronics/bio-imaging. I think both look like relatively interesting majors. However, I don’t know a ton about what each type of engineer actually does on a day to day basis, and I don’t have time to take enough classes to really explore that. I guess in high school you’re not really exposed to the kind of work that an ME or EE would do. What are the characteristics/pros/cons of either field?

Specific insight into these fields in relation to biomedical engineering would also be appreciated.

Also, how much CS is involved in EE? (Or what is the potential for an EE job to turn into a CS job?) I’m pretty good at programming but I don’t want my entire career to turn into just sitting behind a desk coding; that’s not a really good fit for me.

Thanks!