Cough is a reflex initiated by the activation of a subset of sensory nerves innervating the larynx, trachea and bronchi. These sensory nerves are activated by irritants like acid and capsaicin, but also by inflammatory mediators produced in asthma and in viral infections. Importantly, viral infections also produce neurotrophins like nerve growth factor that activate Trk receptors on these nerves cause a sub chronic increase in their sensitivity. This can last for weeks after the removal of the infection, and is much worse in asthmatics. With super sensitive sensory nerves your cough reflex is triggered by even innocuous stimuli. Sauce: I am a professor of neurophysiology who studies this.