First, are you 100% sure about this? I've never heard of a fish being stung by a bristleworm before. All I'm saying is it may not be a bad idea to post a pic just to get a second opinion.
But now if you are positive that the fish has bristleworm barbs in him, then I think if I were in your shoes I would catch him and manually remove the barbs with a pair of tweezers. That is going to be a nightmare (and dangerous for the fish), I know. But I just don't see all the barbs working themselves out.