Hi, I think it is not good in this situation to keep her on some kind of medication all the time. Firstly, I think you should consult her paediatrician and should have her take some immunity booster. In my daughter's case they gave her, Septillin. Also, you can try giving her tulsi water whenever she is thirsty. Have water boiled in tulsi leaves. You know, personally when my daughter had consistent problem of cough, I happen to find a wonder drug for her, or it happened so that it suited her too well. It is Seetopaladi powder. It is an ayurvedic powder with all the herbs in it. You ave to mix one or two spoonful of homey in say one spoon of Seetopaladi powder. Mix it well, and you can give 1/4th spoon twice a day or thrice to your baby. It is best if you give it with warm milk. Let her have it and then make her drink milk. It really worked in my baby's case and hope it does in yours too.
Chk her for allergies..esp note if she has this cough after u give her cows milk or milk laced products...see ur pediatrician