Skin falling off a little?

Lately when I wash my face and arms a little skin comes off. Enough to make a small sore. It's not so noticeable on my face because of makeup but it's painful and extremely disconcerting. It first started about 3 months ago. I had a mole on my face and one morning I woke up and it was red and inflamed. A day later when I scrubbed my face to wash it I felt a pain in that area and when I looked in the mirror I realized I had literally scrubbed my mole off. The skin had completely come off in that spot. Because I didn't have a PCM at the time I just took care of it and shrugged it off. But a couple days ago it happened again. I had this spot on my face that was red and irritated. I didn't touch it thinking it was just a pimple. But when I washed my face again it hurt and I saw that the skin came off. Not a lot, mind you. Not noticeable to other's but painful and irritating to me. I don't know what's going on. I got a new PCM today and I plan on making an appointment but base Doctors are notorious with dismissing people and their worries. Any help would be appreciated!