Waiting until tomorrow won't matter, unless the swelling or pain gets really bad. Immobilize, and make the visit tomorrow. We've had a few broken bones here, and while we got them to ER within a few hours each time, waiting a day would have made no difference at all in treatment or recovery. Our kids just happened to break something on the early afternoons.
When my other son broke his arm doing gymnastics, I think it was about a week before we brought it in. Gymnasts get so tough they don’t react as much to pain. This little guy is no athlete though. I hope he is better in the morning.