That's funny, I suffer from the opposite. Been playing rhythm guitar for years, and the only thing that really brutalizes me is the upper arm and shoulder muscle aches, and only then when the fiddlers decide to get into a speed contest with the dancers. Do that for a 10-minute polka set and OUCH the next day.
Now, how do you flat-pickers manage to make the little plastic thingy behave? I can pick faster and better with my bare thumb, but I'd love to learn to flat-pick...
Best advice for extended back-up playing: stay loose, use minimal muscle power for anything you have to do. Strum mostly with the wrist, fret mostly with the fingers, don't use your bigger muscles unless you gotta (volume sometimes requires power, but if you're doing too much of that, get them to raise your volume in the mix).
OK, I've dispensed enough advice for an amateur..
Keep on Strummin'