I Have Very Dry, Red, Almost Like Chapped Skin Around

I have very dry, red, almost like chapped skin around my eyes and on the sides of my mouth. It is not bumpy, but flakey. My eyes are not dry and neither is the inside of my mouth. Nothing seems to hydrate the skin. My eye doctor gave me an ointment called Neo/Poly/Dex 0.1% OPTH Ointment 3.5gm. I used the ointment last night for the first time and it seemed to help a lot.