Is there a logical reason for getting sick everytime I eat out?

Multiple reasons. It may be due to high salt content of food, preservatives or additives in foods. Even reduced broth may cause unpleasant effects in some people. High fat content is another possible reason for the sick feeling.
Depends. It depends what your are eating. It could relate to gluten or excess glycerol in the flour used in the foods you eat. Restaurants also typically use more salt and fat to cook than you would at home so that the food tastes better.