I am suffering from cheilitis and although I do not think mine is exfoliative I'm confident the remedy I found two days ago can help you!
I've been on (mild) cortisone creams for 6 months now; completely dependent on them too but then decided it was enough. I stopped listening to the doctors because they wopuldn't listen to me; I'd do research for my problem and they didn't give a darn! My mom went to a homeopathy pharmacist and they sent me a kit with a cream called: CALENDULIS.
ONE DOSE and all the little tiny bumps of dry skin went away, the swelling disappeared and I think it's HEALING ME!
I want you guys to know because there is no reason for you to feel ashamed and to want to hide; you are all human beings who deserve love AND an active social life!
It is unfortunate I don't know what to do for fungi (angular cheilitis)... if it is any help, I know ALOE is a potent antifungal plant. It's excellent for prevention...it even prevents athlete's foot from coming back.
If this can help you, I'll be so happy!(as I am for myself right now to be able to kiss, eat what I want and go out!)
Find someone specialized in homeopathy and plants and ask them about CALENDULIS (which I guess is a calendula extract)
If anything new comes up, I'll post again.