Has anyone had this before?

Vanessa

I started having like a dark spot next to my lip then another one under my lip & apparently now it’s growing around my nostrils as you can see. I don’t usually moisturized so yesterday I washed my face and add a Clinique moisturizer and all those areas burn. The one next to my lip gets like dry patches. Should I get it checked at the doctor or should I try moisture it and hydrating serums?