Food Sensitivities in 11 month old

Hi,
My 11 month old has had very mild eczema on his knees as a baby (3 months). This resolved by itself by 6months of age. My baby was exclusively breastfed for 9 months and was thriving. Due to job travel I had to switch him to formula (cows milk based) and he immediately developed a cold and congestion.

I switched him from formula to raw goats milk and the congestion seems to be more controlled but has not gone completely.

He also shows sensitivity to eggs because his bottom turns red and tender to touch after he poops when he has been fed eggs (just eggs yolk not the white).

The congestion has a rattling sound while he breathes and occasional cough during the day and at night and nasal discharge as well which starts as clear and turns yellowish in about 1 week and the cycle starts again.

My baby is a smart, happy, healthy child and started talking at an early age. He said mamma at 5 months (i kid you not!). He is on the leaner side but not skinny but has a voracious appetite with a love for food. Does not like to be left alone, very social, smiles a lot but tends to be clingy to me. He is not a sound sleeper at night and the slightest sound wakes him up. No constipation issues, poops 4-5 times a day, mostly right after a meal or a snack.

I am looking for a constitutional remedy for my son that will treat these food sensitivities for him. Any advice would be greatly appreciated!

Thank You.