Asthma can cause a dry cough. Cough-variant asthma is a kind of asthma that can be caused by the same causes as regular asthma. Dust, chilly air, stress, pollen, and a change in seasons are all triggers. The response of cough-variant asthma to regular asthma therapies confirms its existence. If you continue to cough after taking your asthma medications as directed, you may have something other than cough-variant asthma.