I Started W/a Irritated Throat On Monday Evening. Tuesday Cough

I started w/a irritated throat on Monday evening. Tuesday cough set in. Tried home remedies by Friday I was at the Dr's office. The Dr. prescribed an antibiotic (because my daughter had been to her a few days before w/sinus infection). The antibiotic is Amox-Clav875-125 twice daily. I had not slept for 2 nights she also prescribed PhenPromethazine VC-Codeine Syrup 1-2 teaspoons at night and Benzonatate 200 mg 3 times daily. Also a inhaler, pro air HFA 90 MCG. I slept Friday. Saturday the cough continued and they are spells that almost take my breath away. Saturday evening I took a teaspoon of cough syrup at 10PM another at 11 and another at 1. Today I am continuing w/this cough. I do not have fever or chills. I googled bronchitis and feel I have these symptoms. My question is… should I go to an urgent care facility for an X-ray to make sure it is not pneumonia? I read that w/pneumonia there would be fever and chills. Thank you, Katy Bates