Sacral pain. I feel you there. Having a bout with it myself. Mine usually just flares up from time to time, usually when I try to overdo my stretching exercises or the weather changes. Like around this time of year. Probably not to your extent, but my sacral vertebrae are malformed and just don't line up right. Part of my scoliosis. I wasn't offered the injections for mine, but I wouldn't think they would be all that different from lumbar punctures. Basically the same procedure, different part of the back, smaller vertebrae as you go further down.
Something else you may want to bring up to your doc, the last 4-6 sacral joints (toward the tailbone) are supposed to be fused together by age 35 or so under normal circumstances. That also does not happen to those really bendy people like contortionists. There may be a surgical option there for stabilization if you just have one that's not set right. I'm normally not an advocate of back surgery unless it's an emergency to save the spinal cord or major nerves, (seen too many cause more harm than good) or there's a growing tumor for life saving reasons, but if they are supposed to be fused together naturally, and they aren't for whatever reason, that may make a good case for surgical intervention, depending on where the problem is, and if they can stabilize it properly.
Either way, get pincushioned a few more times, and who knows? You may get some good results from it. It's not unheard of for doctors to be looking in the wrong place for something, and treating the wrong thing for it.
Arthritis, bursitis, scoliosis, sciatica, hip dysplasia, bipolar disorder, migraines, macular degeneration, and probably some other stuff. And they are shutting down hospital departments all over the state, while I'm on a fixed income.
God, grant me the serenity to accept the things I cannot change, The courage to change the things I can, And the wisdom to know the difference.