Bad smell, peeling lips.

Can anyone give me a description and treatment for this
Lip problem. I've had it for about 3 months now. They have a bad smell and it is very annoying due to not being able to eat or drink right. The dermatologist said it was eczema but my doctor said it was Chelitis. I stared with hydrocortisone and it just made my lips soft and practically made the skin so soft it would peel right off and there'd be raw skin. After I saw my doctor I was given an anti fungal cream. I've used it for about a month and I don't see a change. If anyone who has a good explanation please reply and tell me how I can fix this.