Coughing is a reflex that lungs use to expel foreign materials or other irritants. Physicians you can see for a cough can be a primary care physician such as a family doctor or internal medicine doctor. In complicated cases, you may see a pulmonologist for work up of a cough. Most of the time when people cough excessively while they are eating it means that some of the food they are swallowing is going down the trachea into the lungs (going down the wrong pipe) initiating the cough reflex. This condition is known as dysphagia (also known as trouble with swallowing) It is an unusual problem to have consistently especially if you don't have any other complaints. Conditions that can cause this include multiple sclerosis, stroke, and muscular dystrophy. Obviously coughing while you eat is usually not the first symptoms of any of these conditions. I suggest you schedule an appointment with your primary care physician. He or she can take a more detailed history of your symptoms and perform a thorough physical exam. Perhaps your doctor will watch you swallow some water or food in the office to get an idea if you swallowing reflex is abnormal. Good luck.
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Zocdoc