Hello, My opinion is you should not worry, unless you develop difficulty in breathing. How big was the egg piece? Did you start coughing involuntarily after swallowing egg piece? Chances of some thing entering lungs in a normal healthy person is less. Our respiratory tract form nose to lungs have many protective mechanisms to prevent foreign body entering lungs like its anatomy, cough reflex, cilia. If small pieces of foreign body enter respiratory tract your body will try to remove it by cough reflex or it will be trapped by cilia and gradually removed. It will take some time. If foreign body enters lungs, It will cause condition called Aspiration pneumonia If you developed difficulty in breathing, fever, respiratory distress. You should consult doctor. He may request for an X-Ray chest to rule out foreign body aspiration. Hope I have answered your query. If you have any further questions I will be happy to help