Can I buy antibiotic ointment over-the-counter or do I need a prescription?

Yes. There are a variety of antibiotic ointments that one can purchase "over the counter, " like "bacitracin" or "neosporin" or "triple antibiotic ointment." brand names, pharmacy named brands and generic brands are essentially the same, except for price. Some have other ingredients in them like pain medicine. Have your pharmacist direct you to the isle that has the ointments you are looking for.