Not sure if this apply's to anyone else, but the majority of the lip balms are full of drying agents to obviously stimulate more sales. I only got exfoliate cheilltis a couple months back after using Vaseline. Theres a specific ingredient called "Linalool", which i think is a big factor in causing constant peeling of the lips.
After i stopped using products not only with this ingredient in but overall, my lips went through hell drying up and peeling over and over. But i just went through with it, leaving my lips alone and now they are nearly cured.
There will be other cause's im sure, but this ingredient is known for causing eczema, which cant be good if applied to your lips.
Just leave them alone and ride it out. It'll be painful and annoying, but you'll feel hell of a lot better afterwards.