Thank you for all your thoughts and suggestions. To answer a few queries...
It's my inner forearm (just below my inner elbow) where the problem is - I can feel that the muscle is tender there. Although when I'm playing my clarinet, I also feel some pain in my upper arm as well. I did it when tearing paper up in the early summer - a lot of it and quite thick sheaves. (I had a shredder as well, but for each 5 mins use, you have to let it cool down for an hour so I had to tear a lot of it and obviously I didn't realise I was overdoing it). So as well as straining it slightly, there's possibly also a bit of RSI, although it's not burning like I think it would be with RSI.
I just feel silly going to the doctor about this - the pain isn't severe or constant, it's not affecting normal life and the area isn't bruised or swollen. I haven't been too bothered with it over the summer because I've had to give my clarinet a bit of a rest over the summer whilst I've concentrated on "the office move" and all the accompanying hassles, but I really want to do more with it again now and it is definitely troubling me.
My Alexander Technique teacher has retired

She's given me the contact details of her teacher, so I could go to him, or I could go back to my chiropractor, or I could find a physio. In the first instance though, I suppose I'd better go to my GP and rest it in the meantime

Thanks to everyone for talking this through with me and helping me reach this conclusion, and I hope everyone else who's got a similar problem find that it clears up before too long.