What Causes Cough And Runny Nose After Eating Eggs?

My daughter (3 years in June 2014) had been sick now for 9 months with a respiratory tract infection and ear infections. Recently, an X-ray was done of her nose area and she has 80-90% of airway blocked. I have eliminated dairy & Gluten. She is on amox for ear infections/bacteria infection family physician thinks. Should I try taking her off eggs as well as I m starting to notice a trend after she s eaten eggs in the morning.....runny nose, coughing more, asthma like symptoms and coughing more at night time.....Thanks for your help.