Feeding egg whites are fine, I did it a couple times and my fish loved it.

Just remember to cut them into bite sized pieces, or sort of squish them to make then easier to eat. Egg whites are more commonly used to feed fish fry, but feeding them to your goldfish would to good too, a source of protein.
I wouldn't feed my goldfish egg yolks though. Egg yolks are rather high in fat and could cause digestive problems for your goldfish. ^^
~Serenity