Chances at NYU or barnard?

Freshmen year I went to a small School in Tennessee, i received a 3.5 gpa and took no honors/AP classes (weird school, i know). I moved to Florida and sophomore year I took 2 AP classes and all honors, getting a 3.1 GPA. Junior year I did the same and got a 3.5, then we moved again and I transferred to home schooling and started working on my senior year classes also (6 AP’S) i’m getting all A’s and I will be done in December. I am a first generation american and my parents don’t know much, but do I have a chance at those schools? My ACT and SAT meet the average there and before I became homeschooled I did three sports a year. My essays are also very strong and I volunteer often. Obviously NYU and Barnard are reach schools, but do you think there’s a possibility of me getting admitted?

Barnard probably not. You have a chance at NYU though!