If the shot was intra-articular, meaning it was put inside the joint capsule, then I don't see how it could miss. If it was intended to go into a tendon or something, I suppose it could go off the mark, but it could just be that your problems are not ones that cortisone injections would resolve. Also, sometimes long-lasting anesthetic is used--maybe that provided the relief? I had a cortisone shot which came after the knee was aspirated or drained of excess fluid. The relief came from removing the extra fluid more than the cortisone.
Anyway, some people are helped by cortisone, others made worse, others have no reaction at all. Hopefully over the next few days you'll start to experience some relief. However, cortisone is not something that can be repeated often, so keep that in mind.