I would have to agree with the diagnosis, this seems like a case of Asthma (also called Bronchitis).
In view of her severe cough I would urge you to consider getting her nebulized at your local ER/ physician. This would definitely help her cough. I would also ask the doctor to prescribe her Inhalers (Metered Dose Inhaler/ Diskus Inhaler) so that this problem can be managed effectively at home.
In the meantime, ask her to take lots of fluids, steam inhalation, honey and some throat lozenges for relieving the itching in the meantime,
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regards
Dr. Gupta
1 Other Expert Agrees with this!