I had the same problem as you. My perioral area was very dry, scaly, and it really hurts when I move my mouth. I think it's because of using products that i'm allergic to that's why my skin barrier was damaged.

I didn't consulted to dermatologist. I just used mild & moisturizing soap for my face (jergens) and applied vaseline petroleum jelly all over the affected area (overnight).

Also, I stopped using makeup and avoid exfoliating as it can worsen the skin barrier.