I think you will be a strong candidate for just about any university in the U.S. Unfortunately, however, the schools with extremely low admission rates don’t have enough space for the many strong candidates who apply, thus many strong candidates still receive rejections from those universities. Even if your chances are 3x higher than the typical “strong” student, then that might raise your chances to 15-20%, which means that the odds are still not in your favor.
Please make sure that you have affordable schools on your list that you are extremely likely to be accepted to and that you would be willing to attend. Which state do you live in? Many states have programs to help lower-income students attend, and in combination with your excellent profile, you should have many options (in-state or out-of-state). If you need help coming up with schools that would meet these criteria, please let us know.
If you have not done so already, I second @tsbna44’s suggestion of looking into Questbridge.
Also, if you’re interested in suggestions as you help to develop a more balanced list of schools to apply to (beyond the extremely rejective schools like Yale and Columbia), then let us know what you want out of your college experience. What is it that you like about Yale and Columbia? What area(s) of the country would you like to be in (or avoid)? What size school would you prefer? How important is Greek life or spirit surrounding intercollegiate athletics? Are there particular interests you would like to pursue in college (outside of a psych/neuro major)? What would you like the vibe at your college to be like?
Wishing you the best on your college search journey.