Yes eggs can make some people feel nauseous after eating them.
If you feel nauseous after eating eggs you likely have an egg allergy or egg intolerance.
Some symptoms of being allergic to eggs or having an egg intolerance are nausea, vomiting, diarrhea, stomach cramps and other digestive issues.
I would stop eating eggs and tell your doctor that you've been nauseous after eating eggs and they can test to see if you're actually allergic to eating eggs.
Eating the eggs will not kill you but will cause the nauseous feeling or other symptoms that sure don't feel good.
You can also suddenly develop an allergy to the eggs even though you've been able to eat eggs before you might have become allergic to eggs later on in life or have developed the intolerance to eggs.