Scratching

My three month old is still as bad as she was a sour scratching her face and idk what to do except constantly keep her hands covered, but I hate doing that because she likes to chew on them. She scratches the sides of her face repeatedly until I either hold them or she scratches hard enough to make it hurt. Idk what to do, I’ve been using cream on her face because I feel like it might be itching and every now and then her face breaks out (haven’t figured out what it is) but I’m at a loss