Yes. Egg white is low in histamine and is not a histamine liberator, so it is usually fine on a low-histamine diet. Its issues are allergy-related, not histamine-related: it is a common IgE allergen and part of the EoE elimination diet.

Most of the proteins that trigger egg allergy (ovomucoid, ovalbumin, ovotransferrin) sit in the white. That is why people with egg allergy often react more to the white, and why some tolerate the yolk better once cross-contamination is controlled.

Yes. Egg is one of the six common trigger foods (with milk, wheat, soy, nuts and fish) removed in the six-food elimination diet used for eosinophilic esophagitis. Egg white, as the more allergenic portion, is the part that usually matters.