If you are miserable in high school, yes, it’s a good idea. High school is NOT the world, and many people who were social outcasts, or misfits, or just adrift in high school, find their place and are happy and do well in college. There are lots of people who start college at age 17, having been graduated from high school at 17. So beginning at 16 is not that young, in comparison.
There is a very wide disparity in academic level among schools in NY State. You’ve got the best exam schools in the country, like Bronx Science and Stuyvesant (although I think that NYC is trying to change the formula from performance on an admission exam to a more “holistic” process), excellent public high schools in the wealthy suburban districts, and very poor slum schools, and poor rural schools.
But I hear you. You don’t fit in socially in high school, and the academic offerings at your school are not challenging for you.
Graduating early, and going straight to college, unless you have some particular extraordinary achievement, will likely mean that you would not get into the very most selective schools. But you might not have gotten into them, anyway.
As I see it, you have several options. If you can swing it financially, a top US boarding school is an excellent choice. You’re probably going to have social difficulties at any high school, until you go to college and find your people, but I’m sure that you could be academically and intellectually challenged at certain top boarding schools (although since these are the places that the very wealthy send their kids, and the children of the very wealthy are not necessarily brilliant, I wouldn’t be surprised if you found that one of these boarding schools was still not the right fit for you). And the intense social atmosphere at boarding schools can be harder to deal with than at a day school, where at least you go home at night and on weekends.
Another option is to plan to study abroad next year as an exchange student, in a country where you would both be forced to learn the language (you seem to have decided that foreign language study is optional for you - the colleges don’t see it that way), and have access to higher level math and science. This could automatically put you into the “Hmmm, this kid is interesting” pile for the admissions committee. Assuming that the pandemic winds down, doing an exchange year in a French-speaking area with an excellent high school might be a good choice for you. It would solidify your French, so that you could achieve a score that would allow you to place out of further foreign language study. You get out of the social environment of your local high school. As a foreigner, you are interesting, and not expected to maneuver socially at the level of a native.
A third option is to rush through high school, finish a year early, and go to one of the top SUNY schools at 16, probably SUNY Binghamton, if they have what you want to study. Assuming decent grades and test scores, you’d get in. Beware of the option of graduating early and then taking classes at a local state college - they might very likely be at a lower academic level than the AP classes at your high school. BTW, the NYC school system in the past graduated most of its bright kids at 16. It was common to skip a year in elementary, then do 7+8 in one year, and so be graduated at 16.
The most difficult option is to achieve something extraordinary before November 1st of your 11th grade, in addition to plotting out a course program to finish all your required classes by the end of the 11th grade, and apply to and be accepted a year early at a highly competitive college. I’m talking something like placing in the top finalists of Regeneron competition, or winning national or international recognition in your strongest area (published researcher, writer, extraordinary leadership). It’s tough to achieve that in time to put it on applications in senior year, let alone in junior year, but if you can do it by early fall of junior year, it might get you into a very top school, a year early.