You are very intelligent in this inquiry for such a young age. Game programming is within the realm of 3D graphics programming. The common standard is OpenGL, and many programmers use C++. I work with Qt C++ graphics experts.
http://www.cprogramming.com/tutorial/opengl_introduction.html
Such graphics programming also applies to medical imaging or animation and GIS (map software). So you just happened to focus on one of the most exciting and advanced aspects of modern programming that is in extreme demand.
So start with that website. Learn C++ by the end of HS and you will be on your way. There are many C++ tutorials like the one I sent you. There are other websites for OpenGL. It might be difficult at first, but you can get used to the code if you put time into it. Most likely a HS teacher will be more than willing to help you if you show them your research. There is also a lot of help on the forums.
I work with Qt C++ programmers for medical device graphics as a software tester. I've been burying myself in the details of Qt and C++ for graphics. It's fun research, and I get paid lot.
Your enthusiasm for writing can also give you an advantage in programming jobs. Many programmers don't like to write. So if you learn advanced technical writing with programming, you will be in even more demand. Learn UML and how to document requirements, software design, database structures, etc.
I'd recommend listening to the Halo soundtrack while doing the coding. I do. LOL.
http://www.youtube.com/watch?v=1DB4PvAGoIM