It took four weeks, but as of yesterday I can finally hear again. To say that is a relief is a massive understatement, but at least it's now over!
The reason this took so long is largely that every step required someone new involved. As I left things, I'd gone to the GP and gotten something for the infection. Ten days later I was back at the doctor, to find that the infection was indeed gone, and that hopefully it would now clear up by itself. A week after that, with it not having cleared up, I was at another place getting the blockage removed.
And then, suddenly, everything was fine again.