Hello Mummy, I've read somewhere that there can be multiple reasons why babies kept rubbing their faces. It could be because of uncontrolled movement, or like you said a rash or skin irritation. Maybe you can try applying an anti-itch cream or moisturizer and just keep on using mittens so baby won't leave scratches on the face. But for me it is totally normal, but be on the lookout for eczema coz baby is not used to the dry humid weather we have compared to when he/she is still in your womb. Take care always :)