Thanks so much for all of your replies

He's on Neocate which is a fully elemental formula - we tried the hydrolyzed ones with the protein broken down but it still wasn't enough.
He hasn't had any skin allergy reactions, but suffered with bad tummy upsets - he really struggled with gas and poops and screamed pretty much all day until he was 8 weeks old. (That really helped with my PND!!)
We had tried hypoallergenic, lactose free etc but no luck. He's been great since being on this formula. Still had the occasional screaming fit with wind but I think he just gets cramps sometimes.
He's under the care of a Paediatrician, not just a GP. We have a follow up appointment this week actually so will chat to him about solids.
My hubby has nut allergy so I was planning on being somewhat careful about introducing eggs and other potential allergens anyway.