FREQUENT RECURRING CAUGH. Three visits.

My 4 year old daughter has eczema after 6 months of birth, medication does suppressing effect on it and as an when we stop medication it reappears. Her skin is very dry even in summer she needs Vaseline jelly to moisturise her skin. In january she had caugh n cold medication was given for one week than she was normal for 1 week after medication and after that caugh and cold again occur this tym antibiotic was given along with other medication, same cycle happens again this month , this tym i told doc about previous caughs , he told that she had taken a turn towards asthma, he has given medication and told that if it again persist than she will require inhaler course for permanent cure, now again after finishing course of medication the caugh occured so require advise whatbshud be the future coarse of action for this as permanent cure as i have read on net that people having eczema prone to asthma...kindly advice. Also sending u the medication details of last three visits.