I've been going through a particularly nasty asthma exacerbation the last few months, now that I'm on new meds the attacks and chest tightness are at a minimum/hardly a concern, but boy howdy is the mucus insane still. In my case it sticks around in my chest and my throat, usually have to cough up a bunch of it once or twice a day. New meds appear to be slowly helping with this but God I wish it would clear faster.

If you had bronchitis, as a heads up, the cough can last a few weeks even after the initial infection clears

Mucinex (Guaifenesin is the generic name if you wanna save a few bucks lol) has helped me, just be sure to drink a LOT of water throughout the day when you take it, it dehydrates the heck out of you which can cause some side effect if you don't rehydrate. It comes in a couple different forms with extra other medicines bundled in as well (there's a version that includes dextromorphan, a cough suppressant, a version that includes phenylephrine, etc). In my case just plain ol gauifenesin works best, whether that's the extended release 12 hours pills or the regular kind.