If i was told by an allergist that i am allergic to chicken, would i be allergic to eggs too?

Probably not: This is not common, but not impossible. However, if you have been eating eggs all your life without incident, particularly poorly cooked eggs such as runny scrambled eggs, i wouldn't worry about it. However, if you start to notice itching in your mouth when you eat eggs, or get cramping, vomiting or diarrhea after eating eggs, this is suggestive of allergy, and you should start to avoid all egg.

Not necessarily: There is some cross reactivity, however. So it is possible.