Dry skin

Hiya just need some advice, my son has dry skin all around his mouth as its been so cold lately and he has a cold. I think its been too much walking to school and back each day and rubbing it constantly has just aggravated the skin. Ive put sudocrem on and its taken away a lot of the redness but still so dry. Any ideas? My partner apparently had this a lot as a kid as sensitive skin but my MIL cant remember what she did to help it. Dont know if I should call gp as its not a recurring thing and its not bothering him. Hoping to clear it at home.