Yes, a food allergy or food intolerance can produce hand swelling in some (but not all) sensitive people.

When you are told that you might have a food intolerance or food allergy, how do you actually figure out which one you have? Typically, to determine which parts of your diet are causing the problem, a food intolerance diet is started. This means restricting what you eat and slowly introducing new foods. To stay on track, a food journal is used. Other key players in your food intolerance success include a nutritionist, primary care doctor, and a life coach.

Food allergy and food intolerance are not the same thing. Food allergy means that your immune system attacks the food because it is mistaken for an invading organism. Whereas, food intolerance (typically, lactose intolerance) is a difficulty in digesting that type of food due to insufficient secretiion of digestive enzymes (lactase, in the case of lactose intolerance).

The answer is "Food Intolerance"

Yes, you can have an allergy (or intolerance) to food colorings.