The cough reflex expels air and secretions from the lungs with a sudden explosive noise. The cough can be dry and hacking or wet and productive. A coughing spasm is more than 5 minutes of continuous coughing. These infections are called tracheitis and bronchitis, respectively.
Most children get such a viral infection a couple of times a year as part of a cold.
Keep in mind that coughing clears the lungs and protects them from pneumonia. Bronchitis isn't serious. The role of milk in thickening the secretions is doubtful. Usually bronchitis causes a dry tickly cough that lasts 2 to 3 weeks. This is usually a sign that the end of the illness is near.