Since bacteria can build resistance to antibiotics, is it wise to use antibiotic ointments?
It's true that, over time, bacteria can develop resistance to systemic antibiotics-- antibiotics that are swallowed or injected, and so require time to be absorbed and circulate. But that's much less likely with topical ointments, where you apply antibiotics to the skin and they immediately go to work.
You see, the antibiotics in topical ointments are applied at such high concentrations that they usually kill all the bacteria that they come into contact with, so that none of them have a chance to multiply. Also, antibiotic ointments are usually a combination of more than one type of antibiotic. So even if the bacteria are resistant to one kind of antibiotic, odds are one of the other antibiotics will get them.
And don't forget that when you use a topical antibiotic, you're only exposing a relatively small and localized number of bacteria, as compared to the number of bacteria you expose when you use a systemic antibiotic. I mean, you'd have to have a recurring infection, and keep applying antibiotic ointment over and over before bacteria would have a chance to develop resistance--and even then this only happens in rare cases.