K.A.
I am a Respiratory Therapist. You should probably not give your child a cough suppressant. If she does have asthma or a virul infection, the cough is a natural mechanism to keep her lungs clear. A cough that lasts that long should probably be diagnosed as something other than a cold. A medication called Albuterol is used for asthma. If they give her a treatment with this and she wheezes or the cough clears somewhat, then there is a possibility that she does have asthma or reactive airway disease. Is there a family history of asthma? Having her allergy tested is a good choice also.