Do people who have eggs allergy also have allergy to bird?

I have a friend who is allergic to birds and I have to say that it is not a benign situation at all, especially when breathing problem is the main symptom. But I cannot say that he is not eating eggs (although I haven’t seen him eating them either) but I think that the bird allergy is related to the substances linked to the feathers and droppings, I am not sure if it is connected to the eggs in any way.

I have a mild egg allergy.  I can eat foods with a little bit of egg, but not foods containing a lot of egg, such as angel food cake.  I am also allergic to poultry which is worse than my egg allergy.  I cannot eat anything containing even a trace of poultry or I get sick for three days.  I have to read labels in order to avoid all poultry.  It is even in frozen pizza!  :(  However feathers do not bother me at all, but of course, I don't eat them.