Itchy scalp!! Help! 4 month old

Help! What can I do for my baby’s itchy scalp?? He scratches at it like crazy.

I use aquaphor non scented shampoo and Honest conditioner w/ fridababy dermabrush. He has eczema all over his body and cradle cap.

He has a full head of hair. I tried putting aquaphor and honest body oil on his scalp (separately) and it didn’t seem like either of them helped. I also tried putting a hat on him to keep him from scratching and he kept taking it off. I got some oatmeal bath that I plan on soaking him in later.

Side note- he is being seen by an allergist soon but I just need to help relieve his itch. He is having trouble sleeping because he’s so itchy. I’ve been putting hydrocortisone on his eczema but not sure if I should put it on his scalp.