A friend of mine told me recently that whenever she eats eggs, then for about half an hour later she will start feeling drowsy for about an hour or two. She means eggs as in scrambled eggs, omlets, etc. Not the eggs in cakes, unless she has a lot of eggs in those cakes. Does anyone have any idea why eggs can cause drowsyness?

I couldn't find any reference that eating eggs could make a person drowsy.
In fact, this site and several others say that the protein in eggs should make a person more energetic, while fatty foods and too many carbohydrates could possibly make a person sleepy.
Eating a big meal, in general, can also induce drowsiness as the stomach works to digest the load.

I also could find nothing to indicate that drowsiness could be the result of a food allergy.

Maybe your friend just has an unusual metabolism!

Actually, eggs are considered a "snooze food". They contain high levels of the amino acid Tryptophan which a sleep inducing amino acid.

Other foods that contain it are:
Dairy products: cottage cheese, cheese, milk
Soy products: soy milk, tofu, soybean nuts
Seafood
Meats
Poultry
Whole grains
Beans
Rice
Hummus
Lentils
Hazelnuts, Peanuts
Sesame seeds, sunflower seeds

More information can be found here:Tryptophan