a6e96f85__Infections____Their_Treatment__Allergies
[Symptom] Coughing [Cold] A hacking, productive (mucus-producing) cough is often present with a cold. [Flu] A non-productive (non-mucus producing) cough is usually present with the flu (sometimes referred to as dry cough). [Allergies] 
Usually only if asthma present as well. However, if enough post-nasal drainage present, cough can occur even in non-asthmatics.
Flu versus Cold (Upper Respiratory Infections) & Their Treatment
Allergies