Hi M.- I have twins, (now 9 yrs!), and when they were infants, one of them was allergic to soy, eggs, and dairy. I was breast-feeding, and had to eliminate those things from my diet, so it wasn't passed through my milk to my daughter. People with egg allergies can often eat products with egg in them if they are cooked for a long time ( a cake versus pancakes or cookies), because the cooking process breaks down the protein, so the longer it's cooked, the more the protein is broken down. So, you might be able to eat things with eggs in them if they've been cooked a long time.
I haven't heard about a cross-reaction to chicken. I suppose it could be possible. Anything's possible in the allergy world.
My daughter did outgrow all those allergies, by the way, slowly, but definitely by age 2. Avoidance is the best way to help the body heal. Continual exposure to the allergen constantly irritates the body, so it continue to react.
Our allergist's name is Dr. Ann Wang-Dohlman. Her office is located at Newton-Wellesley hosp. Her phone is ###-###-####, if you're interested in working with a pediatric allergist. Good luck!