Hi Julie! Nice to see you and Taffy.
Gill works in the field of Optometry, so she knows whereof she speaks.
I had eye issues with Cinco (obviously), Harvey, and civvie Sasha. Cinco got a Bartonella infection, then Glaucoma and eventually ocular lymphoma. He also had herpes infections in his eyes and I was always having to give him multiple drops. He went blind and one eye was removed due to the lymphoma. The glaucoma and herpes in the other eye defied control so we took it out too. He felt much better after that.
Sasha had dry eyes, which is considered rare in cats, and herpes. In fact, the ophthalmologist that saw her at UCD asked if I would consider allowing them to include her in a study they were doing on the subject. Of course I agreed, and when she crossed, I made sure the ophthalmologist was informed so he could harvest her eyes for the study. She was on a variety of drops and ointments, as well as some serum during her last year.
Harvey had cataracts and glaucoma. He got eye drops, too.
Herpes viral infections are actually pretty common in cats.
Whenever one of them had issues with discharge, the ophthalmologist told me to use a warm, damp washcloth to gently clean the eye.
If your vet isn't able to resolve the issue, I'd recommend taking Taffy to see an ophthalmologist.