When I eat, I get shortness of breath. Is this an allergic reaction or is something wrong with my lungs?

Could be either. Shortness of breath can be caused by either an allergic reaction to something you ate, or could be something wrong with your lungs or even your heart. Could be due to a hiatal hernia or even simple over-eating. Consult with your doctor.
Doctor can evaluate. If a person gets shortness of breath (sob) after eating different types of foods, it is unlikely to be an allergy because one is probably not allergic to so many foods. Sob can be due to lung problems or heart problems. It needs to be evaluated by a primary care doctor, and perhaps a cardiologist (heart dr.). A gastroenterologist (stomach dr.) can help decide if the sob is related to digestion.