This can occur whether or not they test allergic to milk using traditional skin or blood tests. Removing dairy can modestly help those asthmatics who have milk-induced mucus. Of course you will need an alternative source for calcium. Allergy skin and blood tests are reasonably reliable for confirming this type of food allergy, although not for food additives. Most reactions occur because people do not realize they are eating the allergic food.
Chinese restaurants can easily mix a bit of shrimp in with other meals.
Some wines contain sulfites, others do not. Unrecognized allergies to common foods such as milk, egg and yeast also occur. Traditional allergy tests are less reliable. An elimination diet is the best test, but should only be done under medical supervision. Eliminating a food allergen from the diet and then reintroducing it can provoke a more severe asthma attack than the same food might have caused when eaten every day.