I got it from biting chapped lips over many years, I bit the underside of the top lip, where dry bit meets the inside, but mainly the bottom lip, not bothered about the top lip but I have destroyed my bottom lips skin by eating it, trying hardest to heal it though!
Its not infected, if it were your lips would bleed and crack. The peeling means they are healthy it's just loads of dead skin,but the question is how to stop it.