I’m so sorry you’re still coughing. It was awful until I finally got treatment. It sounds like you lucked into a good lung doc. She started you on airway clearance and many pulmonologist don’t know to do that.
The culture results will be helpful and she probably told you the cultures will take 6 weeks.
How productive is your cough? I don’t cough much now and when I do, it’s dry. I’m using 7% saline-new last month because I was sick last winter and he’s thought this might prevent so many URI’s.
I also use a free app called Autogenic drainage-it keeps one on task while deep breathing and ends with huff coughing and I just do the 4.5” one. I started it a couple weeks ago after my little fevers were so persistent after Covid, thinking my lungs hadn’t cleared. They aren’t quite as crackly when I huff cough. It’s gradually gotten down to 99-99.2 for 3-4 hours in afternoon. It’s been 7 weeks-maybe my temp just reset.

I’m sure they told you to exercise daily, too.
Are you still having the sinus drainage?
Acid reflux?
Those can cause mucus/ lung issues. Getting my sinus and allergies under control were the key to me feeling better and decreasing the cough. My CT still has nodules and mucoid impactions etc, but my lung functions are good. I do have mild asthma that caused a little nagging cough, but it responded quickly to steroid inhaler, advair.
Mayo gave me info on postural drainage and some people try different positions while using Aerobika or acapella devices. If did it for a couple months, but started having reflux.
Good luck to you! Keep us posted.