Can you use cortisporin (neomycin polymyxin and hydrocortisone) to prevent an ear infection?

Yes but why?: Using ear drops to "prevent" an ear infection is not wise. You are using a prescribed medication (likely left over) to prevent something that can be prevented without it. When you mention "ear infection, " i presume you mean an outer ear (swimmer's ear). This is best prevented by keeping water out of the ears or if water does get in the canal a couple of drops of rubbing alcohol will do the trick.

No: Ear infections happen behind the ear drum. Cortisporin (neomycin polymyxin and hydrocortisone) won't penetrate past the ear drum and so it does nothing for the middle ear.