Don’t despair. There are still several options left. First, it’s possible that the nerve wasn’t completely destroyed the first time. The body will work very hard to heal or repair anything that’s damaged. Some doctors advise having the procedure repeated a second time.
Second, the local anesthetic can spread beyond the facet joint. This will give pain relief from causes other than the facet joint. For example, if there is a narrowing of the disc space, pressure is placed on the facet joints.
Further testing may help find more answers for you. See your doctor and report the pain you’re having.