Hello and welcome to HCM.
Hepatitis C is never transmitted by cough or any other airborne route.
It is transmitted by
blood transfusion,intravenous drug abuse,tatooing by infected shared needles.
It mainfest mainly as liver problems,cause of cough may be something else.
Treatment of cough depend on presence of other clinical symptoms and duration of cough.
If I were your treating doctor,I recommend,
-Antibiotics like augmentin/
erythromycin for 5-7 days depending on other symptoms presence.(prescription drug).Cough expectorant and steam inhalation provide relief.
-Avoid exposure to second hand smoke or air pollutants.
If the cough still doesnt recedes,may require certain further investigations like CT chest,throat swab,
bronchoscopy.
Hope this information helps.
Thanks.