Thanks for the advice, so far. Happy to get more advice, if it's forthcoming.
I'll try a new battery first. If that doesn't work, I'll get a new HR monitor.
It's a Garmin, but the battery is very easy to replace - I have done it once before when it quit working.
I think it's not atrial fibrillation -- if my HR actually did hit 250+, I think I'd know it!