fur missing around eyes fungus or infection?

Initially, Taro visited the vet due to an injury on his left eyelid which I the vet assumed was an accident (he doesn't have a cage mate). After applying topical antibiotic for a couple days, the injury has healed but I noticed that the fur around his eye started to thin out. I thought it may be him scratching because he has a tendency to do that as soon as I apply the antibiotic. However, ~5 days later I noticed that his right eye started to lose fur around the perimeter. It has been a slow progression and I've dusted him in Tinactin assuming fungus and cleaned the cage with peroxide after dusting him for 10 days. It hasn't been getting better. I'm scheduled for a vet appointment tomorrow afternoon but I would like some input on what I can do until then. I've read numerous posts on here and most CnH members take care of ringworm with Tinactin and cleaning. I thought it might be an eye infection but he isn't weeping nor is there any discharge. Pictures below.

Doesn't look like ringworm to me but it won't hurt him to put tinactin or sulfur in the dust.