Reddit mentions of Abstract Algebra

I'm not sure if you mean abstract algebra or linear algebra, but if it's the former, I liked Herstein's Topics in Algebra. There's also Abstract Algebra by Herstein as well, which I think is a cheaper slimmed down version. I used these books for self study and found Herstein's exposition, particularly at the beginning of chapters, very helpful. He isn't as verbose as your typical 7th edition mass market textbook author though.

For linear algebra, I hear Axler's Linear Algebra Done Right is good. I haven't read it, but I read his paper "Down with Determinants" which is, I think, written in the same style and enjoyed the alternative perspective a lot.

If you are a newcomer to abstract algebra, you might consider using a text other than Dummit and Foote. I used baby Herstein (as opposed to big Herstein) in an undergraduate class and found it to be a good introduction.

You'll remember and forget formulae as you use them. It's the using them that makes things concrete in your head.

Once you're comfortable with algebra, trig. I'm assuming you've had geometry, since you were taking algebra 2; if not, geometry as well.

Once you're comfortable with those topics, you'll have enough of the basics to start branching out. Calculus is one obvious direction; a lot people have recommended Spivak's book for that. Introductory statistics is another (far too few people are even basically statistically literate.) Discrete math is yet another possibility. You can also start playing with "problem math", like the Green Book or Red Book. Algebraic structures is yet another possibility (I found Herstein's abstract algebra book pretty easy to read when we used it in school).

Edit: added Amazon links.