Question: what is the best medicine for a lingering cough?
Answer: Antihistamines, corticosteroids and decongestants. These drugs are standard treatment for allergies and postnasal drip.
Inhaled asthma drugs. The most effective treatments for asthma-related cough are corticosteroids and bronchodilators, which reduce inflammation and open up your airways.
Antibiotics. ... 
Acid blockers.