hey man, this is exactly what happened to me, 100%. this happened for about 3-4 months before it turned into exfolaitive cheilitis for me. it was an alergic reaction to the chapstick i was putting on. i would suggest to leave them completely alone before it gets worse and let nature take its role. if anything, maybe use an all natural balm without chemicals or anything to alleviate the inflammation. trust me, get off that other stuff if your on it. if your on nothing the lips may just be reacting to other stressors. i remember i started wiping them down and rubbing them and using creams which all made it worse until the flakes solidified and turned into a thick peel that never went away, hence, EC. good luck, if they get really dry i just dabbed a little water on them rather then balms.
i also have those spots, which are oil glands i was told and help moisturize the lips. whats strange is that all of us with this condition mostly have these spots whereas most other people do not, so maybe they could contribute, who knows.