After those classes, a typical student would start into something along the lines of real analysis, or perhaps abstract algebra. There are a lot of different math tracks though. Some math majors go all out in analysis, some lean towards algebra, others lean toward geometry or statistics, or actuarial science. It really just depends on where your interests are at and what you intend to do in college.
However, you’re not likely to find anything beyond Calculus III, Differential Equations, and Linear Algebra at a community college. They typically offer other math classes like discrete mathematics and finite mathematics and things like that, but those aren’t really “after” Diff EQ or Linear Algebra. Those are just for people on different math tracks (mainly computer science related fields). In either case, you are VERY well ahead of the curve with your level of mathematics. My main concern would be with the amount of depth in each respective subject. Mathematical maturity is something that comes with time. I’m a math tutor, and I’ve seen instances of students cramming far too much math in during high school. They often learn the stuff well enough to pass the tests, but they often tend to not really “get” the mathematics. They understand how to work through the mechanical process, but they don’t understand what the math really means or see what the equation is telling them. This may not be the case for you, but it’s a point worth considering.
If you aren’t able to find actual courses to take, definitely do some independent study of some more advanced math…but also go back and brush up on some of the math you’ve already done. You’ll thank yourself after realizing how much of it you’ve forgotten. I’m currently tutoring a student in calculus II, and I’ve had to brush up on some of the more obscure methods of integration because I simply haven’t encountered them since taking calculus II myself.