You may have gastric distress when you eat some eggs, they are very high in protein and proteins are a factor in very many food allergy and intolerance issues. The fact that you have difficulty after eating some eggs does not in any way indicate that those eggs contain gluten.
Hen's eggs are very, very widely used in gluten free baking because the sticky proteins in eggs help to replace the sticky proteins left out by not using wheat. We can be absolutely certain that eggs sold in US supermarkets never, ever contain any gluten at all.
When an animal eats foods with proteins their digestive system breaks down those proteins into basic amino acids. In that process all proteins are disassembled. Animals that lay eggs then use those amino acids to create new proteins in their eggs. The body of a hen is not capable of producing gluten. If they could all people with celiac disease would be unable to eat eggs or chicken. That is not the case.
Every single egg that has ever been laid by any hen on the planet in the last billion years was definitely, positively 100% gluten free.
I'm sorry you have difficulty sometimes when you eat eggs, but you have reached a false conclusion by worrying about the diet of hens. Most likely it is the fact that eggs have such a high level of protein that is causing your distress.
