In general, docs don’t want to suppress a cough because they want us to cough out the sputum because it makes a nice home for bacteria.. It’s usually mucus in airway that triggers a cough.
It sounds like your airways are generally inflamed when you’re sick and is probably the reason your doc gave it to you. I’ve had it prescribed a few times and it did nothing! I told my PCP it was useless when I had an URI last year and she said people love it or hate. As I thought about it later, my theory is that my issue is usually increased secretions and maybe those with dry coughs are helped.

Since it helped and rest is important and doc ok’d, maybe use it sparingly and don’t use before airway clearance. I see different half life’s of 1 (most) to 3 hours and its duration is 3-8.

I’d discuss with pulmonologist at next appointment or send message now if you want. I have been offered steroids in past for this type coughing episode and didn’t take them due to bronchiectasis. I asked my pulmonologist next time and he said it would help settle the inflammation and short course would be ok. Good luck. That prolonged coughing is the pits