With the lesion coming and going the way it does, rather than chronically persist, it is likely inflammation brought on by corneal contact with an airborne allergen. The resultant condition is called allergic conjunctivitis, a condition which is especially common now in the middle of allergy season.
While a secondary bacterial infection is often a component of the problem, the primary problem is the allergy. Therefore, a medication that adresses both the inflammatory AND infectious aspect of the conjunctivitis is preferable. Unfortunately, there is no over the counter formulation that will fullfill these criteria. In fact, beyond eye wash and artificial tears, there are very few over the counter ophthalmics, period.
There is, however, an appropriate prescription medication that often provides significant relief for allergic conjunctivitis, a drop formulation called Neomycin/Polymixin/dexamethasone. The neomycin and polymixin are antibiotics that control any bacterial overgrowth, while the dexemethasone is a form of cortisone that is safe to place on the eyes.
I suggest that you call your vet's office and discuss this post, what I think the problem may be, as well as the treatment course I suggested -see if he would be ammenable to dispensing it for you at least to try it. If he refuses, then you always have the option to go for a second opinion.
Good luck. Your cat's problem is a common one. While it is something that you may have to deal with from time to time, you should be able to have the proper medication to provide relief.
Best of luck to you, and thank you for choosing JustAnswer! Please do not hesitate to let me know if I may be of any further assistance.
Sincerely,
Roger L. Welton, DVM
President, Maybeck Animal Hospital
Author, "Canine And Feline 101"