I don't know if you're breastfeeding or formula feeding, but if formula feeding, even the hypoallergenic stuff is made from corn -- and your son could be reacting to that. The ingredients of Elecare are listed at the link below and show corn syrup solids as the first ingredient:
http://rpdcon40.ross.com/pn/PediatricProducts.NSF/web_Ros...
The ideal situation would be for him to get breastmilk (ideally from you - relactate?) and breastfeed well past 12 months while you avoid the foods (milk, soy, wheat, eggs) that trigger his reactions. You can look into relactating, though I don't say that lightly - it would be hard work, and you'd want support from moms who have gone through it, but is certainly possible (many adoptive moms do it) and sounds like it might be worthwhile given the health issues he's experiencing:
http://kellymom.com/bf/adopt/relactation-resources.html
I think the formula companies and many doctors do us moms a huge disservice by trying to pass off formula as a decent substitute for our babies - while it is for SOME, it is really detrimental to others. My kid would NOT be thriving on formula (even hypoallergenic) given his multiple allergies. Human milk is tailor-made for human babies (cow milk is for baby cows, soy milk formula and corn syrup solids making up hypoallergenic formula are not as healthy as human breastmilk - even the formula manufacturers agree to that! - and while some kids do fine on formula, some do NOT and really, truly just need their mother's breastmilk). Plus, it is more likely that he will outgrow these allergies over time if he's getting breastmilk. Yes, it can at first seem challenging as the mom to limit our own diet (if breastfeeding), but it is worth it when your baby is calm and comfortable and happy - it is definitely do-able and becomes really 2nd nature once you get the hang of it (reading labels). I've had to do this for my DS, now 10 mos - very obvious cow milk allergy, likely soy too though I gave that up when I cut out cow milk products, and I also suspect a sensitivity to wheat. My little guy doesn't seem to have the egg sensitivity that yours also has, but I can absolutely empathize with you and your little guy.
A great book is Dr. Doris Rapp's "Is This Your Child" which is specifically about babies, kids, and allergies. Best of luck to you - I really hope our babies outgrow these allergies!