Has this happened with your cat and what did you do to cure it?

I think it bothers me more than her and it was much worse when I first got her several months ago, but there is this black stuff around her chin which its only obvious when using a very fine toothed flea comb. It looks like flea dirt but definitely is not.

The Vet said it’s a type of dermatitis and stop using plastic food dishes. I did that immediately, but it keeps coming back. I’m wondering if Peroxide might help? Or is there something else?
I’m assuming alcohol might be too strong.

I’m trying to avoid another Vet visit for such an apparently minor issue since I recently shelled out around $250,00 for something that really was a life and death issue which seriously put a dent in my budget.

Anybody else dealt with this?