4 month old continuously scratching self?

My 4 month old son has eczema. I keep it under control pretty well for the most part. I also trim his nails every 2-3 days. Yet he still manages to scratch himself so badly it looks like he got attacked by a cat! No matter how often I trim his little fingernails he can still manage to scratch himself and sometimes it bleeds. I'm assuming he does it because maybe his skin itches from having eczema? But even when he's not having a flare up (which he pretty much never has them anymore) he still just scratches and scratches. His scalp is the worse! I moisturize his scalp twice a day with Aveeno for babies to keep it from getting dry and itchy but he scratches it and it looks terrible. He use to wear mittens but for the past month he pulls them right off so he can suck on his fingers and of course scratch. I hate taking him out in public because I'm so afraid someone will think I'm a bad mom. Any suggestions? I'm at a loss :(