This is an interesting question because of the fact that it seems to come back every other month. It is also unfortunate, and hopefully it can be resolved quickly.
The important thing to know is how long you have had this for, what things are associated with it, what do you do before it comes every other month, and, possibly most importantly, what it looks like (which is why you will need to see a primary care doctor
for a complete answer). The fact that it gets better with the antibiotic ointment could imply that it is bacterial in origin, but, without seeing it, I would guess that it might be more likely to be related to the moisture that is in the ointment. Does anything else (specifically, other creams or gels) help to make it better? Does anything make it worse? The fact that it comes every other month makes it seem less likely to be bacterial as well, unless you have some reason to get a bacterial infection on your face routinely (such as acne, which can lead to breaks in the skin that can then get infected). Even so, this is generally associated with other symptoms, and a simple antibacterial ointment might not be sufficient in many cases.
Please see your family doctor
or dermatologist for more ideas. In the mean time, keep your skin well hydrated, and see if you have any improvement.