Exfoliative cheilitis, Google it. (the pictures there can be a little scary) It's when the skin on the lips grows hard & then peels off leaving raw skin behind. Currently, there's no universal cure for EC, although it can be managed & even cured with different methods. However, what works for one person won't work for another unfortunately, that's why this condition is so hard to cure. Mine was caused by constantly biting & picking the skin off my lips until they were raw. This is my 5th year with this & it's been hard to deal with.
I'm not sure if you actually have EC but the sooner you heal the better or it will get worse. I'm currently trying Colloidal Silver & will give an update in a few weeks.