Eczema and food allergy

Nya

My LO has been dealing with eczema and extremely dry skin since he turned two months old. His skin is very flaky, dry and it completely changed color ( he’s dark skinned but he looks light skinned now). At his 4 month check up his pediatrician order a blood test to check for allergy. I told his pediatrician that he was scratching his face a lot while feeding, and that he would breakout in hives. Turns out he’s allergic to eggs, and I was eating eggs almost every day. Since I found out about I’ve stopped eating eggs. I also decided to give up dairy and gluten since many people who’ve had eczema experienced skin improvement since giving up certain foods. LO’s skin is improving significantly and his dark skin is slowly starting to come back. My problem is I’m not sure if my new diet is helping him, so far he’s weight is average and I would very much want him to gain weight. Any advice?