Several things come to mind here:
For students who are considering medical school as one possible option it is a very good idea to keep an open mind regarding other possible career paths. This sounds like something that you are already doing.
Public health can be combined with other related majors such as nursing or medical school. Again this is a good plan.
Premed classes are tough. They are tough at any “top 100” university, and probably at any “top 200” university. The competition will be very strong at any very good university. At Cornell the competition may be particularly strong in these premed classes. You are not deciding whether to enter Cornell as an average Cornell student versus starting at one of your safeties as an average student. It is more likely that you could be deciding between starting at Cornell as an average student (or possibly slightly below average on GPA) versus starting at a safety perhaps in the top 25% of students. It really is not clear which would improve your chances of getting to medical school, and probably would not make much difference one way or the other.
Which has a stronger public health program might be a very different question.
Medical school is expensive. If you want to keep it open as an option, then make sure that you budget for a full 8 years of university. If you qualify for a lot of need based financial aid, then Cornell might be relatively affordable. If not, then it it unlikely to be your most affordable option. If you are full pay, then between now and the day that they call you “doctor”, it could very well cost over $800,000 and might approach $900,000. You do not want to take even half of this as debt.
Neither daughter was premed. Both however had majors that overlapped a lot with premed classes and knew quite a few premed students (at least two of whom now have an MD). I have heard multiple stories about how tough these classes can be, and how strong many of the premed students are even at a university that is not quite ranked in the top 100 in the US. Let me know if you want to hear a few examples about the rigor of premed classes.
And to me it sounds like you are doing very well, and we are really just hoping to help you think about what might be a good fit for you.