I can only give my experience having dealt with lip swelling and burning much like yours. I believe the problem is caused from inflammation within the digestive tract. For the past 1.5 months I have been following a vegan diet and I can't believe the impact it has had on my lips. I never thought I would say this but my peeling has almost stopped happening now. The peeling would customarily start with rawness/redness of the inner lips together with dry cracking along the top of the outer lips, like yours. The reason I suspect the dermatologists have not been of any help is because they are not trained in health or nutrition, they are trained in disease and they lack a somatic understanding of the human body. This is why dermatologists supply creams and lotions to treat a problem elsewhere in the body. I would say that you have digestive issues, your guy flora is out of sync, your body is reacting badly to something you are eating, attempting to heal the damage caused from it via inflammation. Inflammation is the bodies way of healing damage. I would suggest you research veganism and implement it soon and also purchase some aquaphor and apply it routinely to the lips to keep them moist. SO far I have been doing both of these things and I am having tremendous results. I'm also waiting for probiotics to come, I think this will be the final nail in the coffin for the peeling lips. My lips having been peeling for 15+ years !