my infant won't stop pulling out his hair.

Casey
My 4 th month has eczema in his scalp and has been pulling his hair out while he sleeps. At 1st I thought his hair lost in the back of his hair was due to his sleeping on his back but after 2.5 months he pretty refused to sleep on his back anymore. While monitoring him at night I noticed him scratching his scalp to the point where he was drawing blood. Also about a week ago I noticed his sides of his hair starting to thin out. And of course the sitter told me he had begun scratching there too. Has anyone else experienced this? At his 4 month checkup the pediatrician said use T-gel 3x a weeks and have him wear mits/socks while sleeping. He also prescribed steroid oil, not a fan of using it on him so young. Does anyone have any suggestions. Please help. I'm about to pull my hair too. I attached a before/after pic s so you can see what I am talking about.