Coughing during drinking is a concern. I would strongly recommend that you see your doctor
to have this evaluated.
This biggest concern that one has when hearing about coughing while drinking is that of aspiration. Aspiration is the medical term for when food or liquids go down the trachea (the "air pipe") instead of the esophagus (the "food pipe.") This event of "going down the wrong pipe" is a concern. When the found enters the lungs it causes some irritation and therefore the body triggers the cough reflex to clear the airways.
This is a big concern. Food or liquids going down the airway is concerning as this can result in pneumonia
. Aspiration pneumonia can result as bacteria that normally live in the mouth can enter the lungs and cause an infection. In addition, the acid in the gastrointestinal tract can enter the lungs and cause a "chemical burn" or aspiration pneumonitis.
The fact that you have it with liquids, and not solids, suggests that there may be a neurologic cause. The swallow reflex is a complicated series of events that any nerve damage can alter and cause aspiration. When people have problems with solids we often think of a mechanical problem.
I would strongly suggest you see you doctor as this is a concern.