My daughter who is 3.5 years old have cough problem for one month now. she started coughing more on early morning. we use asthalin inhaler some times.

I think you nailed: the problem...using her inhaler only "sometimes". Asthma is a chronic condition with acute exacerbations. There are medications for maintenance of clear, open airways & medicines to use when airway spasm & inflammation occur. Your pediatrician may chose to manage your daughter's asthma or refer her to a Pediatric Allergist/Immunologist or Pediatric Pulmonologist, if if proves difficult to control.

OneMonthofCough=TTYD: Does she have seasonal allergies? Chronic cough that tends to be worse upon rising often is a result of post-nasal drip - that can occur due to allergies or sinus infection. It could also be that her asthma is acting up. In any case, she needs to see her pediatrician so that they can sort out the cause of her cough and the best approach to manage it.