As we age we lose some of the tolerance we had for certain foods because our bodies lose the ability to digest them. Some people become gluten or lactose intolerant as they age, for example. It's unfortunate but, considering the alternative, we have to learn to live with it (I can no longer tolerate raw or partially cooked broccoli--which I love.) and moderate out diet. This may be what is happening to you in re to eggs. I seriously doubt that the addition of an extra cell from the rooster has anything to do with it. You may find that if you wait and eat the eggs later in the day, after your digestive system has adjusted to having food in your stomach you will not have the problem.
BTW, I don't know about Italians but the main ingredient of French cooking is butter, butter and then more butter. That artificial stuff can kill you.