Coughing non-stop for about 1 week. Deep / rhaspy productive cough with discolored phlgem. Phys asst put me on amoxicillian. No improvement. Ideas?

Possibilities... There may be a bronchospastic cough complicating the acute bronchitis picture. A sputum culture can determine if the correct antibiotic was chosen and a bronchodilator inhaler and a steroid inhaler can be added so the bronchospasm will be controlled. These steps should improve the cough. Good luck!
Time to be rechecked. Persistent symptoms with no improvement with treatment deserves a recheck. Cough could be due to persistent post nasal drip from a sinus infection or allergies. Additionally, an upper respiratory infection (usually viral and untreatable) could be a cause. Lastly, a bronchitis, pneumonia, or asthma is also possible. Follow up with your doctor or pa to see if additional treatment is necessary.