The 620 on the English is about 75th%, and would surely be good enough for your state college, maybe good enough for your flagship state U, depending upon what state you are in. I’m not surprised, because your writing is pretty good. I bet you have been a reader. I’m assuming that your math score was much lower, since you’re keeping it to yourself. Yes, you might be able to bring it up with self-teaching. But you don’t have to self-teach the math. You don’t need an SAT to start at a community college. They are very good at fixing the gaps in students’ math preparation - they have an entire stepped, progressive curriculum for it! It’s pretty easy to teach a willing, motivated person math, assuming that they don’t have a serious learning disability. It’s much harder to make up for the lack of 13 years of reading that they should have done, in order to become a literate person by college - fortunately, this is not the case for you.
Your goal should not be studying for acing the SAT! It’s just a test. Your goal is to get an education, and become an independent, fulfilled, self-supporting human being with a good, happy life. Sometimes when we’re up close to something, we have trouble with stepping back and seeing the big picture. The SAT is the up close, narrow focus view. It is an appropriate means for a home-schooler to demonstrate that they have had an excellent homeschool education, since they lack the verifiable GPA and transcript from a high school. In your case, the math score shows that you haven’t. Step back, and see the big picture. You haven’t had a conventional education, and trying to make your education fit the conventional route to college at this point, especially since you’re anxious about the social transition to college, is not the best idea. I think that your best bet is to register for community college as a high schooler, starting this semester, if it’s not too late, and otherwise for summer or next September, depending upon what is permitted, as a homeschooling high schooler, with these classes being considered dual enrollment for high school. They have a remedial math class sequence that you can take, in addition to lots of other classes. You could do at least two semesters, maybe three at the community college as a homeschooling senior, and then quickly finish your Associate’s degree there and transfer to probably your flagship state U as a junior, and do two to three years there, to get your BA.
This route has a number of advantages. You can take all sorts of classes next year, plus their remedial math sequence to fix the gaps in your math education. You can get a driver’s license now, and have a year of driving under your belt, before you leave for college. You could get a part time job, and gain the maturity that comes with that, before you leave for college. You can get comfortable with the group classroom model for instruction (which involves speaking up in class, going to office hours, asking the TA or Prof for help if you need it, forming study groups with the other students, learning how to get hold of your textbooks without having to pay hundreds to thousands a semester - all skills that you will need for college). Think of next year as training wheels for college.
Then, if you’re just destroying community college, and you feel that you want to try applying to college via the traditional route, for a traditional freshman year experience for fall 2023, you will have that option. Or you can just finish the Associate’s degree and transfer to whatever school best fits your needs and your budget. It’s a cheap, low-risk means of filling in the gaps of your home-schooling education, while giving you the opportunity to gain more maturity.