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Cough is not associated with problems with the thyroid. Symptoms of an significantly enlarged thyroid gland would be difficulty swallowing or possibly problems related to the airway, but as stated the gland would have to be enlarged and pressing on the other structures in the neck.
The other symptoms would depend on whether the hormone level is low or high. If high, a person may experience symptoms such as palpitations, tremor, weight loss
, intolerance to heat.
If it is low, then symptoms such as weight gain, constipation
, sensitivity to cold, dry skin, fatigue, hoarseness
and muscle weakness
A cough in a viral illness can potentially last up to 6 weeks. Since it is dry , you can consider using a beta agonist to help with the cough. These are sometimes combined with other cough medications or can be taken on their own, they reopen the airway. Closure of the air way is one of the reasons for coughing.They may also help with the tight sensation in the chest, this feeling can also be due to airway closure.
i hope this helps