As a granny now, with quite a lot of hindsight, I offer some humble advice.

My eldest son was like that too from the moment I brought him home until he was 3yrs old when his little brother was born and I was advised to not use any fabric softener in the laundry.

The poor little blighter was ITCHING! A baby feels pain all over their body, only when they get older does pain become localised.

Another reason I discovered, with HIS children, was too tight or too much clothing - like those "babygrow" outfits. Could be the infant is feeling claustrophobic?

Stay away, also, from "baby oils" of mineral oil content - use pure cold-pressed virgin olive oil on their skin - it prevents dryness and itching.

Feather pillows or duvets could also be an irritant.

Good luck.