There is no “better” med school. All med schools are good - the difference is at the residency level.
Almost all freshmen who intend to be premed (sth like half to three fourths) give up. Support is thus crucial, as well as advising. Support and advising is necessarily weaker at a public university (that’s the type of thing you pay for when you attend a private college with strong academics.) The smaller schools have better support, hence better odds for you.
You shoudl absolutely apply to FIU and FIU honors, AND a few other colleges.