My baby's been developing small welts and redness on his face, looking a little like rash. What causes it?

Infantile rash. This could be a number of things depending on the age of your child. Anything from erythema toxicum neonatorum to infantile acne are all potentially possible. I would recommend you have your pediatrician have a look first, and if your child is behaving like he/she is sick then sooner than later.