3mo old and scratching at his face...i say talk to the pediatrician, at 3mo and doing that doesn't seem normal. I understand when they are newborns and doing that but 3mo is odd. Talk to the dr see what he says. It could be an allergy making him itchy.
Yes what they said^^^ my baby use to do that especially when she had gas...
Also if you don't have mittens at home some times baby socks are better. :)