Deciding what to study at undergraduate level

I'll second the recommendation for bioengineering, that's exactly the field you're describing.

However, you might find at the undergraduate level that you'd be better off studying something that will get you a very solid foundation in mathematics and computer programming, which are the languages bioengineering uses to represent and model the behavior of biological systems.

Being an interdisciplinary field, it's critical to balance your time spent learning the various sciences to become an effective bioengineer. You need to have an understanding of very different areas of science such as cell biology and fluid mechanics, so you can integrate these ideas together in your research.

In my experience, students with a background in physics, mathematics, or chemistry actually do better in graduate level bioengineering courses than students whom studied bioengineering or life sciences as undergrads. The formerer were learning to solve complex problems and represent phenomena with mathematics while the bioengineers were memorizing facts and nomenclature in biology classes. Memorizing biological facts is much easier to pick up on your own when you need it, whereas math proficiency is a skill that must be developed over years of practice.

Many prominent professors of bioengineering actually have their degrees in the physical sciences, and taught themselves the relevant biology.

The most important advice I can give is to start doing research in your field of interest NOW. Even in high school, you can volunteer to work in a professors lab. Performing research is where the real education occurs, not in the classroom.

I'd go with Biomedical Science. If you plan to study those kind of subjects at graduate level, you need a lot of experience in the lab as an undergrad. You're going to need to do a summer internship in a lab and a lab-based final year project if you're going to have any chance of getting into a PhD programme when you graduate. If I were you I'd email the types of graduate department you'd be hoping to join after your undergrad studies and ask them what they look for. I think you'll find that practical experience is very high on their list. It's not too early to start thinking about where you can get that kind of experience either. It's a highly competitive field and the more proactive you are the better your chances.

There's a field called bioengineering.

I don't know all that much about biology / subsets, but some general academic advice: it's always easier to roll down than climb up. Find what you think is the most challenging approach to where you want to go, and start there.

Bummer your U. doesn't have an explicit bioengineering. As an undergrad though you should be fine. The basics of engineering and biomed are pretty set especially for the first two years. Try to get these, concurrently start learning about what bioengineers do. In the best case, get summer jobs either with profs doing bioengineering research (doesn't have to be at your U. but that is easiest if it exists) or even better with companies. This will inform your education goals and you can even quiz the people involved on the topic.

You should also take up a team sport. If you are intelligent there is a high likelihood that in a few years time you will be applying to Investment Banks, Management Consultancies, etc., and nothing (other than a high status university & good people skills) will help you more.

Tissue engineering is another cool field - that's making and developing scaffold tech for growing replacement (or presumedly novel) organs and limbs, s'far as I know.

Don't make a definite decision until you have to. Most universities don't make you have to decide on a major until sophomore or junior year. Use your first year as an opportunity to take classes in different areas that seem interesting. After you've done that, you'll have a much better idea deciding what to major in.

Perhaps nanobiotechnology?