Why does my skin do this & how can I fix it?!

Hello.

I recently had really dry lips, and with that came really dry skin around them. I got rid of the dry lips, but no matter what I do, the dry skin doesn't go away. I usually use Vaseline on dry skin, but it didn't work. I have Vaseline lotion, I put that on, maybe, 5 min. ago. The area around my lips turned red & started to sting. It went away now, but why would it do that? And how can I get rid of the dry skin?

Thanks : )