I suggest that you rinse the egg-concoction off your hair with conditioner, instead of shampoo. Also, don't use hot water. Rinse your 'egged' hair with tepid water on the sink. And then, apply conditioner as you massage your scalp and gently comb your hair with your fingers. After at least, 15-20 minutes, rinse off the hair conditioner. Do not scrub your hair to dry with the towel vigorously. Just pat or damp-dry your, now clean and soft, hair gently.
Thank you for asking.