First and foremost, no one knows your child and what is normal for her better than you. So trust your instincts. It is obvious that you watch your child's symptoms closely which is very helpful in determining the seriousness of the illness. Coughing is good in that the lungs are trying to clear out the phlegm. Lots of liquids thin and moisten the phlegm and soothe the throat, so make sure the child gets plenty to drink.
Cough syrups containing expectorants also help bring up the phlegm.
If coughing is keeping the child awake at night, look for cough syrups that contain a cough suppressant. Check the calendar.