Egg allergy is a rare cause of these symptoms. Tests can be done to check for it. Please meet an allergy specialist

Respiratory allergies alone are rarely due to any food.

Need more history Kindly schedule an appointment with detailed history and online examination to come at accurate diagnosis. This history not enough to give a definitive answer

Visit physically to nearby pediatrician.

Hello. The symptoms you have described point more towards an allergic rhinitis instead of egg allergy. This is commonly due to exposure to household allergens like - dirt, dust, smoke, pollen, animal hair/feather, artificial food colours etc. So try to avoid exposure to these elements first and note the change in your child. Egg or any other food allergy is often associated with nausea, vomiting and stomach pain. There may even be a complaint of loose motions. The respiratory component normally gets involved in extreme cases and usually its more of a breathless picture rather than a stuffy nose.

Kindly consult once physically to nearby pediatrician

Can be Treat it properly and if it gets better then not necessarily due to eggs

Consult with Pediatrician physically for further evaluation and treatment