It's great that you have a lot of these things out of the way already! But I'd like to repeat other people's comments about how well do you actually know the material in classes you've taken. I've found that a lot of lower-level classes are computationally focused and don't actually require a deep understanding of the concepts described in class. Have you tried explaining what you did in class to someone else? But I definitely do think it's easier to understand a more rigorous treatment of a subject once you have a first exposure that let's you get a bit of basic intuition.
Have you taken any combinatorics or elementary number theory classes? They're a great way to teach you how to think mathematically without getting bogged down by abstract definitions (although one could say that this is later an important part of "mathematical maturity"). The reason I mentioned this is that I really hope you don't get turned off by all the abstraction that happens in a lot of topics in theoretical math before have some idea of what thinking mathematically is like. You could also try reading about complexity theory, algorithms or related fields in theoretical computer science. Also, have you heard of
http://www.artofproblemsolving.com/ or math contests (e.g. math olympiads)? I think they're quite good for the same reason as I mentioned about learning some combinatorics (i.e. easy to understand problems, but interesting solutions). Another thing is that you have something you can use to check your understanding, which is really useful if you don't have a friend/mentor to discuss this stuff with. You mentioned that you're interested in double majoring with physics. What kind of physics are you interested in? That could provide some direction on areas of math to learn more about (unfortunately I don't know much physics at all).
From classes you've already taken: It looks like analysis, complex analysis or abstract algebra could be courses you would be able to take next. However, I highly recommend taking some time to learn how to think rigorously before you take them (take a look at some books in these subjects, e.g. Apostol, Stewart, Rudin, Stein & Shakarchi). Since you still have so much time left, it would be a nice idea to try to read these texts at your own pace and maybe write a blog or something trying to explain what you've read to yourself. I don't know if it's the best idea to rush through high school, but I guess it depends on how interested you are in other subjects or working on your social skills like others have mentioned. That having been said, I think you should probably /not/ stay in high school if you find it boring/like an endless time loop. Most importantly, have fun!