Eggs can make you feel sick because of the sulfur. Sometimes the sulfur can be hard to digest and upset your stomach. If you have a rash, hives, vomiting, or nasal inflammation you might have an allergy or sensitivity to eggs. Try to not eat eggs for a few days and then reintroduce them to your diet if they make you sick again discuss this with your doctor. Egg allergies can cause intestinal discomfort but they are rarely life threatening.