It ultimately depends on what you're looking for. Private institutions are not necessarily superior to public ones. Honestly, if you want to apply, just apply and see what you want to do from there. Privates might be harder, which can tank your GPA for med school applications, but also bring a bit of prestige to your file. It's a weighing of odds. Given that you have a few medically-related service hours, why not consider a BS/MD program? I know that USF and UF have some.