I broke my scaphoid bone, but it didn't hurt too badly. I wasn't sure if I broke it or sprained my wrist (I had never broken or sprained anything before, at least to my knowledge*). It was a Sunday, so I just went to the grocery store and bought a wrist brace. The next day (Monday) it still hurt, so I scheduled an appointment with my regular doctor for the next day (Tuesday). Tuesday morning it didn't hurt all that badly and I considered canceling my appointment, but I went anyway. She sent me for X-rays and they found that it was broken. Scheduled an appointment with a specialist the next day (Wednesday), and he told me I could just keep wearing the same wrist brace for 6 weeks.
So it took me three days to get to a qualified doctor, and he told me to do what I did the first day.
YMMV
* In retrospect I may have broken the same bone (or perhaps the scaphoid bone in my other hand) years earlier on my first attempt at downhill mountain biking on a ski mountain. I came into a clearing and saw my friend stopped for some reason - turned out there was a ditch running across the hill that I couldn't see very well, and he was trying to warn me. My front tire went into the ditch and stopped, but my body kept going. I'd estimate that I flew about 20 feet and my bike landed about 10 feet past the ditch. I went to the ski lodge, got some ice and went back up, but it hurt like hell. It hurt for a while after that.