I suppose that there is bad news and good news.
The bad news is that your GPA does seem low for an Ivy League university. The good news is that if you want to get accepted to a good medical school, as others have said it really doesn’t matter whether you attend an Ivy League university. There are hundreds of universities and colleges in the US that have very good premed programs.
I happen to know a couple of doctors. They have told me that the various students in their MD programs had gotten their bachelor’s degrees “all over the place” (this is an exact quote from one of them). I happen to know someone very well who got a different medical-related graduate degree (actually two master’s degrees) at Columbia, and she also reports that the various students in her program had gotten their bachelor’s degrees at a wide range of universities. My older daughter is currently getting her DVM in a highly ranked program, and again reports the same thing. I listened in (via zoom) to her welcome ceremony while they introduced the incoming students and said where they each had gotten their bachelor’s. Nearly every student had gotten their bachelor’s at a different university (there were a small number of repeats, but not many).
The fact that you already have some medical experience is a good start. You SAT score is also very good.
Premed classes will be quite difficult at any “top 100” and probably more like “top 200” university. The classes will be full of very strong students, there will be tons of homework, and exams will be tough.
Doing well in these tough classes will be important for acceptance to medical school. So will the experience that you get in a medical environment. So will your MCAT score (and if you have been able to get 1560 on the SAT, this suggests that you can do very well on tests). So will your references.
Medical school is expensive. Budgeting for a full 8 years of university is important. Avoiding or minimizing debt for your bachelor’s degree is important. Since you come from New York, you have the good fortune that you have multiple very good in-state public universities which should be relatively affordable for you.
Yes, it is very good and will prepare you very well for medical school. Also since it is in-state for you it might be relatively affordable (although how much aid you might get if you do get accepted to an Ivy League school will depend upon your family’s financial status).
Where you go to medical school and how you do in medical school will be way more important. Again, if you look at the top medical schools, or at any MD program in the US, you will find students who got their bachelor’s degree at a very wide variety of universities.
Educating your parents might be a difficult task. You might want to talk to your guidance counselor at school and see if they can help. However, I have seen many, many, many people attend “pretty good” universities for undergrad and then attend very highly ranked universities for graduate programs. I got my master’s degree at Stanford (which is not Ivy League, but which I think would impress even your parents) and the other students in the same program had gotten their bachelor’s degrees again at many, many different universities. With one exception I never did meet two students in the program who had gotten their bachelor’s at the same university, and the exception is not ranked in the top 50 in the US.
You can apply to a few Ivy League universities for undergrad and see how you do. However, Stonybrook, and the other SUNY’s, are very, very good for premed students and can set you up as a first step to do very well in life. Also, if Stonybrook ends up being less expensive compared to let’s say Brown or Columbia, then you might be better off getting a bachelor’s degree at Stonybrook and saving some money for medical school.
Also, when you go to a hospital, you will see a large number of medical professionals, and many of them will help you or me when we are patients. Most of these medical professionals are not doctors. They are still very important. You will not see some other medical professionals, such as the people who work in labs to analyze whatever samples they take from you, and the people who are doing biotech research which might lead to better treatments in the future. There are many good jobs that do not involve getting an MD, but which nonetheless can both lead to a good career and will help people. My younger daughter is doing biotech research and has been doing very well. If their effort succeeds (a big “if” in biotech research) they will help a LOT of people. There are a lot of options other than medical school. You are likely to get some sense of what some of these are when you are in university.
I think that you are doing very well. You do not need to attend an Ivy League school to continue to do very well.