It should, but if you're that interested in going to a competitive program, why set your sights on just being a high school instructor? Spend a few years in college and see if you feel the same way about what you've "known for a long time".
Also: physics physics physics. Don't even bother with math unless you want to double major. A physics degree usually carries at least a minor in math, the real kicker being of course that you can actually DO something with math.
College physics opens so many doors, an MS is usually more than sufficient to teach various college level courses in the subject. Be warned though: this is a difficult subject. It's not at all uncommon for people to switch majors or get burned out.
A few top physics schools off the top of my head (and in no particular order): Cal Tech, MIT, U. Chicago, U. Colorado @ Bolder, Harvard, Cornell, Ohio State, UC Berkeley, UCLA, UC San Diego, UT @ Austin, Stanford, Dartmouth. I could go on but the AIP actually publishes lists for these, as do many sites.
Many of these schools get plenty of 4.0 and high SAT applicants, so have other ways of placing yourself above the other applicants. Being a woman is a plus, but show them that they want YOU at their school. Attend some SPS meetings while you're still in highschool. If you're near a university, go to their physics seminars whenever possible. A huge part of physics (and life it seems) is just learning to speak the language and schmoozing with people in your field.
I find the following is great motivation: Books by Carl Sagan and Richard Feynman. You should find your own personal role model, but these two are wonderful. Good luck!