What Causes Dryness In Nose Along With Dry Cough?

My wife. White female age 55. Dry nose dry cough. Sinus plugged. Draining in back of throat. Mucus clear when she can cough some up. Has used a nasel wash. Taking remron and xanax and lamical, ibefrofin. Did go to a urgent care and placed on amoxicillim 2 weeks ago