Hi ScienceGurl,
In modern society, a professional astronomer is the same thing as an astrophysics. The field uses physics to describe astronomical events. NASA does hire some civil servants as astronomers/astrophysicists, but mostly they employ contractors through universities and science-related institutes. A scientist who wants to receive funding from NASA will usually apply for a grant under a specific project. According to the talk I heard on Tuesday by the NASA Astrophysics Division Chief, NASA's astrophysics budget is around 9% of its total budget, and that is expected to remain consistent for the next for years.
In the United States, there are over 100 colleges/universities that grant astronomy or astrophysics degrees. Much more common are colleges that grant physics degrees but also conduct research and offer classes in astronomy/astrophysics. Check out the websites for any college you're interested into see if their program matches your interest. You have lots of choices!
A doctoral degree is a common requirement for most astronomy/astrophysics positions. There are jobs out there in the astro field that do not require a Ph.D. Since you're still in high school, I would recommend you wait until you have some college experience before deciding if you want to pursue an advanced degree.
This webpage may help you get an idea of what an astronomer/astrophysicist does:
http://www.astromiror.org/research.html#astro . Most of those interviewed work for or with NASA, and all of them are female.
Good luck! And don't let anyone tell you that you can't do it!
Laura