My name is Kim de Groh and I am a Sr. Materials Research Engineer at NASA Glenn Research Center in Cleveland Ohio. I have been conducting research art NASA for 20 years :). Ill try to answer your questions from my experience.
When I was in high school, I also loved math - it was my favorite subject (in addition to art). I took a chemistry class and (I think) a physics class my senior year in high school (oh - so many years ago), but I actually didnt do very well in those classes when I was in high school. But, since I did well enjoyed math, while in high school I thought of getting a math degree.
When I first attended the university, I signed up for a science math based residential college called Lyman Briggs College at Michigan State University. At Lyman Briggs I started taking chemistry physics classes, along with math, right away as a freshmen, and I found that I really liked those college courses (different topics better teachers than my high school classes). But, after my first college calculus class I decided that I did not want to major in math (too theoretical). Because I was really enjoying my atomic physics and chemistry classes, but I also liked math art, I decided to get an engineering degree.
If you choose any science/engineering based major it will be beneficial to have chemistry and physics classes in high school, but I dont think they are necessary, in that you can take them as a freshman as part of your core curriculum classes at college, prior to starting your major subject courses (which usually start your junior year). So, if you dont have Physics AP in high school, you can take the required physics classes while at college. On the other hand, if you do take chemistry (and physics) in high school, and dont major in those fields its still good because youll need basic chemistry physics for pretty much all engineering disciplines.
One thing I did that was really helpful, and I advise you to try to do - if it is an option, is to take an introductory class into different engineering careers. It was through taking a one credit Introduction to Engineering Careers class that I was introduced to the different types of engineering careers and first heard about materials science, which I thought sounded really interesting. So I decided to try materials science as my major, and loved my classes the related research, and I love my materials work here at NASA!
Another very helpful thing for me was to get summer jobs in my field, as this helped confirm my interest in getting a degree in materials. Perhaps as a high school senior, you could try shadowing different engineers in your area to learn about different engineering disciplines, and the types of tasks they do.
I hope I helped answer your questions. Id be happy to answer any more you might have.