Persistent dry patch of skin around lips

I thought it was my normal dry skin/chapped lips that I get when it’s cold, but it will not go away no matter how much I moisturize. What can I do to make it go away?

I thought it was my normal dry skin/chapped lips that I get when it’s cold, but it will not go away no matter how much I moisturize. What can I do to make it go away?