The Color of Grass
My guess is that your excitement to race through school is partly due to a low valuation of your current high school experience, including boredom and social isolation. College and the real world surely look like places where "the grass is definitely greener." It's possible that you will never value other human relationships as highly as the average person, and thus, racing through the phases of life is an optimal strategy for you. But I would bet that at some point, you will value those relationships much more than you do now, and find yourself in an awkward position. You see, high school and college are stressful and chaotic times, socially speaking. But they are also essential to building your social skills, because you will likely never be in a situation where you have so much close contact with people your age. Once you get into the working world, the spread of ages increases, and the level of social connection decreases. It gets harder to meet people the older you get. If you compress this time by 50% or more, you will likely look back on it one day and think: "Perhaps I should have spent more time meeting people and socializing back then. There were so many opportunities."
Completeness
It's easy to focus on the things we're good at, and avoid the things we are not. That is human nature. But if I had to guess, your mom is quite possibly worried about the scenario I'm describing above, but not explaining it as clearly as she could. Can you survive as a pure math prodigy? Well, there's Grigori Perelman (I did enjoy his biography). But unless you want to become a hermit, you will need to become somewhat well-rounded. At the very least, you will need to be able to communicate clearly with others, especially in written form. And if you choose to go into industry rather than academia, you will almost certainly need to learn some application of mathematics. I strongly second Sue's suggestion to study some Computer Science. You may find that programming suits your personality well (and gives you a lot of career choices later on). Odds are, no matter what path you choose, having some programming skill will be useful to indispensable in the future, so this effort will certainly reward dividends.
It's good that you mentioned the SAT. Obviously, having poor grades in non-math subjects does not bode well for potential scores. You don't need a 1600 to get into good schools, but performing poorly on the reading/writing section will not work in your favor. As I said before, communication will be an essential skill for the rest of your life. Spending an adequate effort developing this skill by reading broadly and practicing your writing is an investment that will only yield strong positive returns. There is nothing more frustrating than having a brilliant idea, but not being able to explain it to others. If you're slacking in your English classes, just pretend that English is a somewhat broken formal language, and use computer science skills to turn it into a math problem. That might help with your motivation. But reading outside of math is also important to become a complete human being. It's good to go deep (learning as much about one topic as possible), but it's also important to go broad (learning a little bit about as many topics as possible). Yes, you can do both; and there is no right answer about the optimal balance. But you will find that the most successful people in any field (including pure mathematics) almost all have a broad range of interests and pursuits, even if they have gone very deeply into one of them.
Learning
I find that the best way to learn something new is to pick a goal and work towards it. Try to find some concept that interests you, and learn everything you need to understand the state of the art in that area. Sometimes you will encounter an enticing side trail, which you should follow. Sometimes, you will discover an even more interesting problem that you didn't know about when you started, and you will shift your focus. The important point is keeping yourself motivated. If you're getting stuck on a concept, it means you have gone too far, and need to go back and study the fundamentals. Nailing the fundamentals is essential in every field and skill. But practicing them for their own sake is not terribly fun. That's why it's helpful to "go deep" first, and find a problem that motivates the need for stronger fundamentals. This then gives you the motivation to back and learn something better that may have seemed boring at first glance.
Where to get ideas? Well, StackExchange is a pretty decent place to start. Just browse random questions on the Mathematics SE (which I assume you already do), and look for ones where the answer involves concepts you haven't encountered yet. Chase the ones which sound most interesting, and your plate will be full in no time. It's not unusual to find math-heavy questions on Physics or Computer Science or [Electrical] Engineering or Aviation, so it's worthwhile checking those out as well (and helps with the "going broad" strategy).
One of the reasons that going broad is such a valuable strategy is in the nature of learning itself. Ultimately, the abstract reasoning which separates humans from most other animals comes down to generalizing across distinct ideas. It's about finding connections. It's about looking at an apple and a tennis ball and a rock and thinking about what makes them different, but also what makes them the same. Your brain will do this for you all on its own, as long as you feed it lots of data. And the more diverse the data, the more connections you will discover. Many fruitful ideas come from cross-field collaborations, where people studying ostensibly unrelated topics end up finding an unexpected connection that helps them understand better. It seems hard to believe that your pure mathematics skills could be improved by studying biology or aviation or economics, until you realize that partial differential equations well describe many phenomena in all those fields, and having physical instances to visualize and reason over strengthens your mathematical intuition about the equations themselves.
Conclusion
If I were you, I'd make this deal with your mom:
Mom, I'm learning math much faster than my high school classes can possibly teach me. Sitting through them is a waste of my time when I could be productively learning maths several years ahead. On the other hand, I recognize that I have not been as diligent in my other subjects as I could be, but that these subjects will be more important in the future than I have given them credit for.
Thus, I propose this bargain: you let me test out of all the math I can and take whatever college math courses are available to me, and I will raise all my other grades to at least a B. If, at any point, my grades fall below a B, I will withdraw from my college math courses. Is that fair?
Finally, I would recommend that you try to socialize with a broad distribution of your high school peers. You surely find that you have little in common with many of them, but learning the strengths and shortcomings of your fellow humans and members of society is most certainly a skill that you will use for the rest of your life; and the better you are at it, the happier you will be, even if you end up cloistered in an ivory tower inscribed with Greek letters. That includes playing a sport, if you don't already. "Balance" is about developing the body as well as the mind (and physical fitness improves your brain function). Team sports are especially good, because few activities teach you how to cooperate with others (including exercising and following leadership) than playing on a team.
IMO, your best strategy is to learn as much math as you can, anywhere you can, while still spending 4 years in high school and 4 years in an undergrad program where you can fully develop your non-math skills and exploit the wealth of social opportunities that you will almost certainly never again encounter in later life. Good luck!
