I feel for you, because I've had the same experience my whole life. I'm not an M.D. so I can only speak for myself, but eventually I learned that it was absolutely critical to not cough. Otherwise I would not get better or it would take forever. Almost all over the counter cough medicine is a combination of Dextromethorphan and Guaifenesin. Guaifenesin is an expectorant, which means it makes people more inclined to cough, which is appropriate if you have phlegm build up that needs to be eliminated, but that was not my scenario, so it was actually making the problem worse. I'm pretty sure I had pleurisy a couple of times over the years, it's a miserable experience.
Eventually I found cough pills that are just Dextromethorphan and when I feel an episode coming on, I start taking them. A lot of them, like one every two hours. It's been highly effective over the years. Sadly, when "robotripping" became a thing, my preferred pills became somewhat hard to find and pricing is all over the place.