One thing I need to clear up, the coccyx DOES move, which I misstated that...it's the sacrum that is solid. I got overly focused with the term sacrum. Still, go with what the doc said, that you fractured it but the treatment would be the same. A fracture there cannot be casted, cannot be immobilized...so he's right, no need to have a picture (unless you personally want it), and it should heal up with moderate treatment. By the way, a fracture takes awhile to heal and so it will be painful during that time, decreasing as it gets better. You might want to go to www.spine-world.com and look at the illustrations they have for the spine, they're informative and might help you understand your situation better.
If this thing doesn't noticeably improve in a couple weeks, you can always go down to the Urgent Care and have them do a plane black & white X-ray of your lumbo-sacral spine, ask for just two views, and keep a copy of the pictures and report somewhere, for future reference if needed. Also, take a photograph of the bruising, keep it with the X-rays if you get those. See, there is a small chance that (a) it won't heal right, or (b) you not only tore up the end of your tailbone, but that the impact hurt your lower spine in some small way. So, if you have to get further treatment down the road, the X-rays and photo will help whomever treats you.
But basically it is indeed true, no need to X-ray because the thing will heal up on its own. It's a solid bone there and won't be moving around. It's only if it doesn't get better that the doc would get a scan. By the way, if you wind up getting an MRI, keep in mind it's cheaper to get a CAT scan.
And I personally think if the pain is really bad, then don't hesitate to ask your doctor for medicine that will work better than the stuff he gave you...he can call it in for you at the pharmacy, or you can get a squeeze-in emergency appointment tomorrow if you like. And if I were you, I'd tell my employer I fractured my lumbo-sacral spine and you need a few days off because the pain is so bad right now. Then just lay around and give yourself a break, let it heal up better. Heat helps pain, by the way, so put a hot water bottle in that spot.
An x-ray won't show very much and will involve unnecessary exposure of your testicles, so your physician gets two points. Good for discounts at Home Depot.
These injuries usually heal on their own, but take time and can be very painful.
After a suitable period of time, if the pain does not subside, he will probably order an MRI.