Go meet with your guidance counselor again. Talk about your academic history, and your improving grades. Find out how those old grades were transferred. Find out when you are on schedule to graduate from high school. For example, some students need an extra semester or year if they transfer in from a foreign educational system. Get your counselor’s advice about how to frame your future college application. If your school has sent a lot of students to NYU your counselor will know what your chances are there. If your school hasn’t sent anyone to NYU, then of course your counselor can’t be much help about this.
If you have formal records for your mental health issues, then yes, your counselor can comment on that in the counselor’s letter that will go out with your application. Your health issues affected your performance those years, but now that the health issues are resolved, your performance reflects your true capabilities.
You also can plan now for a gap year. That way when you apply to college, you will have your full high school record available, not just the grades for this improved junior year.
In any case, keep up the good work. You will have more and better options with good grades than if you decide to slack off just because one particular university isn’t a possible admit. Think about what it is that you like about NYU and where else you could have a similar educational experience.