Why does poached egg make me sick?

There could be something about the way you are cooking the egg. Some poached egg recipes call for vinegar. That could upset your stomach if you are using such a recipe. Maybe you aren't cooking the eggs thoroughly. For a quick (if not very pretty) egg poacher, you might try one of the Nordic Ware microwave poachers, with no added ingredients except a little shot of cooking spray. It takes about 90 seconds to cook 1-2 eggs.