M.G.
Are you sleep deprived? I'm guessing so if you have a 2 month old. Are you rubbing your eyes or are they irritated because you're tired? I get red, sore eyes if I am tired. My eyes will burn and feel itchy.
Dematitus, reaction to a product or soap you're using on your face, allergies, etc. If it's bothersome and not going away, and spreading - I'd be careful not to use same towels, etc. as others at home and I'd go in.