Eczema baby cannot sleep

Hi all, our son is now around 5 mths old. He has eczema and egg allergy. From time to time we try our best get him away from anything that would cause itchiness to his body. It comes and goes. But recently his face and possibly head scalp has been flaring up. We try to use Dermeze on the face which helps him soothes and scalp we use some baby oil. We are having issue that he keeps constantly scratching his face and its worst after midnight and essentially he won't stop and constantly flaring up those skin from face to head. The only way we can put him tonsleep is to wrap him up which is not recommended way of sleeping especially at his age. We are not sure what to do next or if someone has similar experience. Our eczema baby will constantly scratch face and head in circular motion during day and night. Please help. We haven't been able to sleep after midnight smoothly as he would wake 2 to 3 times between midnight to 7am and it is very difficult to put him down. We are going in circles on this and lack of sleep doesn't help us with any of his morning activities. ;(

Desperate from some guidance