I used to have a cough like that. In my case congestion during the night would get me coughing in the morning as my sinuses drained and then I couldn't stop coughing all day. Finally kicked it by refusing to cough. As stupid as it sounds it worked. The coughing was making my throat sore which caused me to grind my throat trying to clear phlegm that wasn't there, which in turn made me cough more. Vicious cycle. By paying attention and refusing to grind my throat or cough it gradually got better until it finally went away.