There are really no “Pre-med” schools. “Pre-med” is just a term students hang on themselves to indicate they are studying to apply to medical schools. Very few colleges have a “Pre-med” degree, although some do recognize a “Pre-med” course of study.
Medical schools require a 4-year bachelors degree (it can be in anything) as well as a few basic science classes like Biology, Chemistry, Organic Chemistry and Physics, in order to apply.