More often than not, youngsters outgrow these sensitivities. Sometimes it's around one year or two years, and occasionally it takes longer. I've never been much of a proponent for milk introductions at 12 months but since you are very astute and aware of the reactions, you'll know when your child is doing fine with these foods. As long as he stays fine, it's OK. If you notice reactions again, he'll have a better chance of outgrowing the sensitivity with 100% avoidance for some good lump of time.
There should be no immediate reaction to the miniscule amount of egg in a vaccine when a child's reactions are intestinal, but I do worry sometimes about a child who shows a great propensity for developing allergies; that a new or renewed allergy could develop. The way scientists create food allergies in rats, to study in laboratories, is to inject them with a bit of the food. That makes me just a little wary in terms of injecting certain things into a child with greater allergic potentials.