Hi,
No, you wouldn't have hurt the rectum/anus, but the nerves in that area are "connected" for function and pain. If you're in pain, it would be difficult to "bear down" for a bm....even for holding in or contracting the sphincter to prevent urination or bowel movements. If the nerves are damaged, impinged or affected in any way....you will have pain with all the functions with which those nerves are involved.
As far as the pain you're having now....as we heal, some parts start functioning better than others. If some are functioning to capacity and the others are lagging behind, they're not maintaining the load so to say and become fatigued or overloaded and pain will result.
It seems normal what you're experiencing, and I can definitely relate to your pain. When I was a child, I always tended to fall on my tailbone. Either from skating or on the icy roads/sidewalks. My doctor feared I might suffer permanent damage if it persisted. Luckily I "grew up" and was a bit more cautious about my balance on those surfaces.
It'll take a while for you to heal. But, if it persists maybe meds can help get you through this worst time. Caution about some pain meds, they can cause bowel bleeding and/or constipation.
Another option could be accupuncture to stimulate nerve pathways and help the healing process.
Hope this helps.
quincy