I can remember having this problem for a number of years now. I went to doctor and he said just put moisturizer on it. After a couple of years I got referred to dermatologist and she couldn't offer any advice or help and just said it doesn't look too bad so just leave it. My next appointment is 1st Feb.
There is a ring around my mouth where the skin is a different color and no hair grows. If I don't put moisturiser on it it gets flaky and painful. Some days it is worse than others. It looks like a pink ring around my mouth.
here is a picture