Since high school I've gotten menstrual cramps bad enough to occasionally send my body into shock: nausea, cold sweat, feeling like I'm going to pass out. This week it happened at work (and let me tell you, it's awkward to tell your boss in the middle of a staff meeting that you need to go lie down on her office floor before you fall out of your chair). But I was pleased that my body gave out long before my mind did - I used to be terrified of the pain, but now I can handle it a lot better.
As a social worker, I spend a lot of my workday coaching people on how to cope with stress. I think I deal with physical pain better now because I know more methods for handling it.
So, when you're waiting for the painkillers to kick in, the doctors to splint your leg, or whatever:
Self talk
Pay attention to whether your inner monologue is "This is horrible. I can't do this!" vs. "I can get through the next half hour, and then I'll go lie down." Coach yourself through it like you would coach a child.
Distraction
Sing songs to yourself, do multiplication facts, count ceiling tiles. Pick an object and describe it in all the detail you can: "That cinderblock has eight dents near the bottom and a grey smudge near the top left corner." Focus on your breathing. Repeat a phrase to yourself: "This is going to be okay."
Stimulation
In some article which I now can't find, I read that the brain can only process so much nerve input at a time. So additional sensory input can theoretically reduce the amount of pain your brain is processing. I found that drumming my fingers lightly on my palms seemed to help.
Placebo effect
Even when the tylenol you just swallowed can't possibly be in your bloodstream yet, try thinking about how very effective and quick-acting it is. You may get a small placebo effect just from believing in it.