I have had a very severe cough (vomiting, stridor) for over 10 years. Despite a lot of investigations and a lot of medications, I still have it and the best diagnosis they can come up with is "hyper reactive upper airway". I can tell you that severe coughing has always caused social disgust, and I know you are right to worry about the reaction of others now that everyone's tolerance for coughing is lower than it ever was. As suggested by
@drron, I always apply a mask as soon as I start to feel the tickle. That helps manage other people's anxieties.
Then I ostentatiously pull out and use my Symbicort (Budesonide) inhaler and once I can talk again, I tell people it is asthma, even though it is not. Asthma is something the average punter thinks they undersand. The linked article
Still coughing after COVID has passed? Here's why — and what you can do about it suggests Budesonide is the go to medication for a long covid cough, and has other suggestions to help manage coughing. Maybe you could discuss this with your doctor, and if they think it is indicated, you could try the Symbicort, both for symbolic and practical reasons. I do find the Symbicort gives me relief when the coughing is dreadful.
Perhaps also get a doctor's letter outlining your circumstances? And I always answer "no" to COVID apps and questionnaires that ask if I have a cough. If you say yes, there is no one around with enough medical knowledge to make an intelligent decision - I found this out the hard way when going to hospital to have a bronchoscopy to investigate my cough and I said I had a cough and they refused to admit me - yes really. My procedure was cancelled at the last minute, had to be rescheduled and my specialist told me to always say no and argue the toss later if ever questioned about it eg "oh I thought it was asking me if I had an undiagnosed/untreated cough."
I wish you all the best with this very difficult issue.
