Final answer:
The next step in the management of this patient would be to perform sinus X-rays. The patient's history and examination findings suggest that she may have chronic sinusitis, which can cause a chronic cough.
Step-by-step explanation:
The next step in the management of this patient would be to perform sinus X-rays. The patient's history and examination findings suggest that she may have chronic sinusitis, which can cause a chronic cough. Sinus X-rays can help to confirm this diagnosis and guide further management.