I would recommend you follow your math track at “the nation’s second best” HS. I would not self-teach a subject that is such an important building block for future coursework in advanced math, physics etc. Instead I’d suggest you focus your time and energy in doing the best you can in all of your actual classes, making meaningful contributions to ECs you care about, and studying for standardizes tests when appropriate.
Then self studying in advance is seriously a waste of time that you could spend building your EC’s. Use supplemental resources like Khan Academy concurrently while enrolled in the course.
The way colleges work is that you pay them money and take classes. They are also looking for people who have taken a calculus class really have a foundation in calculus. So if you take calculus in High School with a teacher who independently evaluates you, that is the type of student they want in general.
Join (or start) a math team, compete in the AMC (look up “American Mathematics Competition”), study up for the Math II Subject Test, or tutor lower level math to kids. You should plan to take calculus at your high school, but that doesn’t mean you can’t try a statistics class at your local college on the side. There is a lot you can do. But do take the classes to make sure you have the right base.
If the OP is a sophomore in algebra 2, s/he will will take precalculus as a junior and calculus as a senior. I.e. already on the +1 math track. No idea why the OP wants to self study it when s/he will end up having it in school anyway.