I’ve had exactly the same thing, constant cough for more than 3 weeks, I didn’t feel ill or anything just an irritating cough. It took a good 4-5 weeks for the cough to dissipate.
With the news reporting this new ‘variant’ of covid, I thought it could be that. I tested multiple times though without a positive result.
I feel for you Steve, it was a right pain in the ass. I can’t imagine what it’s like trying to record a video with such a cough!
P.s I like a drink too, I stopped drinking for a few days and noticed my cough died down a bit. Alcohol lowers the immune system.