Brief Answer:
yes it certainly can..

Detailed Answer:
Hello XXXX, Welcome to HCM..

I've gone through your query and understand your concern..

Yes, what you've explained, is quite possible.. let me explain it to you so that it'll be clear to you also..

Due to sinusitis and infection, the secretions got stuck in your upper respiratory tract(starting from your nasal passages to various para nasal sinuses etc.), along with that there's inflammation also.. So when you started exercising, there's increased effort of breathing through all these already blocked(partially) areas and with forceful breathing during the exercises these area get pulled and stretched too, thus resulting in heavy phlegm and throat tightness..

What you experience during flying(that crackling noise) is basically due to partial opening and closing of your eustachian tube in side your middle ear (it's the tube that connects our middle ear to our throat)..

It can be seen normally also, due to drop in cabin pressure during flight take-off as well as landing.

So next time your boarding a flight make sure to swallow (try to swallow your own saliva) as much as possible it'll help, putting earplug will also help.. but most importantly, try to board the flight after getting cured of sinusitis and influenza because these are the condition which aggravate this problem..

It's good that you've completed the Z-pack course, but since it has returned again, i'd advice you to continue Z-pack for another 10 days after discussing with your doctor..

Also start taking steam inhalation three times a day..drink plenty of warm liquids like porridge/soups/hot menta tea etc., they'll provide soothing effects as well as help in healing faster..

Decongestant tablet containing Phenylephrine can also be started in view of sinusitis and phegma, please discuss with your treating doctor..

Hope I've cleared your queries, I'd be happy to clarify if your having any further doubts..

Take Care
Kind Regards

---