Curing stubborn cat acne?

[u/mollskis]

I first noticed my cats chin acne a few months ago. Since then I have been trying switching to metal bowls that are always clean (no more plastic), cleanser for cat acne with a warm compress, taken him to the vet twice and they gave him antibiotics and coconut oil. It goes through periods of getting a bit better and I think something is helping but ultimately it’s still much worse than when I first noticed it.
He is constantly rubbing the affected area on whatever he can, I’ve heard it can help to make sure everything is clean but my house is already very clean as I live with my mum and cleaning is her passion and I have also seen him doing it outside in the garden. I was thinking maybe I should talk to the cat about using a cone to stop this? But he is also an excessive dribbler which I can’t really control and this of course gets all over his chin. If he’s just eaten and had whatever else in his mouth and starts dribbling I can’t imagine it’s helping to heal the acne.

Im curious if anyone else had this situation and found a solution that worked? I assume it bothers him and the rubbing is due to it itching so I hope to found something that works soon.
Thank you :)