The gripping hand, actually, seems to be exactly the problem. I saw the doctor about my right wrist today, X-rays were taken, and the conclusion is there's no bony injury or anything of that nature; I haven't fractured anything without knowing it. His working theory is that it's a repetitive-stress injury from gripping and using my cane.
Treatment, for the moment: I need to watch how much weight I put on my cane, and I need to pad the handle, or fab a new handle with padding built in (possibly easier and more effective). In the meantime, for the next week, I'm on anti-inflammatories.  A LOT of anti-inflammatories. 800mg of naproxen sodium, three times a day, with meals. (I suppose this means I need to eat three meals a day for the next week, something I don't usually do -- I'm used to eating two meals a day, sometimes only one.)