C.C.
From what you're describing, he may just have very sensitive skin. One of my girls is this way. She was allergic to Dreft, fabric softener, synthetic fabrics, heat made her break out, she would get hives ALL the time, she was sensitive to dairy... on and on it went. Poor kid. The good news is, although her skin is still sensitive, it's much less so than it was when she was a baby, so they DO grow out of it!
What I would do is remove potential allergens one by one until you find the culprit(s). Change to a scent-free, hypoallergenic laundry soap. Rinse his clothes an extra time before drying. Don't use fabric softener. Those are all really hard on newborns. If you don't notice an improvement, then go to dietary - sorry mama, but you may have to go dairy-free if you're breastfeeding (or go to a soy formula if you're bottle-feeding).
Also, as time goes by, he may just get over it on his own. It really doesn't sound much like eczema (which would be almost scaly looking), and if it were acne, you'd know (it looks just like teenager acne).