I find it difficult to evaluate your GPA. I see a GPA of 3.9, but am not clear on how it is calculated. Also, you say that your rank is third. I interpreted this to be that there are two students in your grade in high school that have a higher GPA, and everyone else has a lower GPA. This also leads to the question of how many students are in your grade (third out of 20 students is not quite the same as third out of 300 students). I was thinking of a normal sized high school, with a few hundred students. At least where we live, in the local public high school, a GPA of 3.9 would not put you third in the high school. To me this makes it a bit difficult to predict your chances because I guess I do not quite fully understand all of this. 1360 on the SAT is something that I know how to interpret.
Regardless I think that Brown, Yale, and Amherst college are unlikely. However, I agree with @tsbna44’s comment “so what?”. You can do very well with a bachelor’s degree from Rutgers or U.Mass. Since you are in-state for Rutgers, it is likely to be less expensive for you unless you qualify for a lot of need based aid, and this means that you might be able to save some college funds to help pay for medical school (or for some other graduate program).
I understand that Brown, Yale, and Amherst College get a higher percentage of their incoming freshmen into medical school. However a lot of this, and I would suspect possibly all of this, comes from the consistent academical ability, work habits, and determination of the students who get accepted to these schools. You will find quite a few equally strong and equally driven students at Rutgers and U.Mass. The strongest students will just not be quite so ubiquitous at these schools.
To me the most important issue is to make sure that you are applying to at least one solid safety that you can afford and that you would be happy to attend. I am hoping that Rutgers fits this description. I am not completely sure however whether either Rutgers or U.Mass are safeties. I think that both are likely, and both are very good universities for students who are majoring in psychology with a premed intention.
If you are going to add one or two schools to your list, I would add schools at the safety end of the scale.