Skin experts: Dry skin around the mouth problem?

Exfoliate. Use the Philosophy Microdelivery Exfoliating Wash. It has micro beads in it that buffs away dead skin. The first time you use it, your skin might get a bit red, but afterwards your skin will be used to it. Don't use sugar or something like St. Ives because they have big beads with rough edges that is unsafe for any skin type to use.