Ds1 is currently hors de combat with a broken wrist - he's 15 and did it by falling about 10 feet (doing stunts on his bike). His wrist was swollen and sore, but the first aider at the skate park said they thought it was sprained, not broken - we disagreed and took him to casualty. Sure enough, he's in a cast now.
Ds2 has broken both wrists - on seperate occasions. Once playing 'Prison Rules Football' at senior school (apparently that's football with NO rules.
The other time he was mucking round at home and fell over - and as others have said here, we didn't think it was broken that time - there was a little swelling but no deformity, and though he did whinge about it, the pain seemed to settle with calpol, and he slept fine that night. It wasn't 'til the next day, after he'd been out playing football, when he tried to boost himself up onto the worktop and collapsed with pain, that we took him to casualty.
Actually it was dh who took him - I was up to my eyes in emulsion, redecorating our bedroom, when dh came in and said, "Ds2 is still whinging about his wrist - I'm going to take him up to casualty so THEY can tell him it's not broken." Half an hour later he rang to say he'd be back when ds2 had had a cast applied.
If it is broken and he needs a cast, you might find that they won't put a full cast on it at once, because they might be concerned about further swelling. Each time one of mine has broken a wrist, they've put on what's called a back slab - basically a slab of plaster under the arm, bandaged onto it, to stabilise the fracture. Then a day or two later, they put on the full cast.
This was done as an outpatient in the Fracture Clinic for ds2 both times but ds1 had to have an anaesthetic because he'd displaced the fracture and it needed manipulation under anaesthetic, but this was a very quick process, and he was so alert and well on his return from theatre that he spotted the dinner trolley and ordered his sunday lunch on the way past on the theatre trolley!! Roast lamb, roast and mashed potatoes, gravy, sweetcorn and trifle to follow!
If I remember right, ds2 had his plaster on for 3-4 weeks each time, and ds1 is expecting to have his taken off in 6 weeks (because he did a proper job of it, I assume). Neither of them seemed to be in agony afterwards - ds1 has used neurofen for pain relief and went back to school on monday - two days after the accident and one day after the op. He did wonder if he'd be able to do his paper round, provided he switched his brake to his right handlebar (he's broken the left wrist) but we didn't think that was a terribly good idea!
I hope your ds feels better soon.