This is a very interesting question without a perfect answer. The quick answer is that you cough may be caused by hypothyroidism, but a dry nagging cough has many more possible causes which are more likely than hypothyroidism.
The typical symptoms of hypothyroidism are cold intolerance, fatigue, hair loss, weight gain, depression, constipation, and low heart rate among others. Cough is listed as an unusual symptom in patients with hypothyroidism and while it is possible, there is very little clinical data to absolutely say for sure.
Coughs going on for a few weeks are mostly related to an infection such as a cold or bronchitis
. It can also be related to common medications taken such as those in the ACE inhibitor family. Asthma
and gastroesophageal reflux can also be causes of a nagging cough.
I suggest you schedule an appointment with your primary care physician
who can examine you, review your symptoms and order the needed tests to see whether or not you even have a hypoactive thyroid gland. To do this you'll need to have blood work done to look for your TSH level. This is the only way to determine if your coughing and other symptoms are possibly related to your thyroid. Good luck.