Does Cold And Cough Indicate Sign Of Asthma?

My chil is 4yr n 10 month old she has cold n cough but no fever.doc has prescribed clavam,sinarest,n calpol.but her cough hasn t relief,the he advised ambrodil s,she is now much better.but has told me that she might have asthama.is it really a case of asthama or allergy?