It depends why your wrist is hurting. If you have a structural or non-inflammatory wrist problem then injetion often does not help. inflammatory problems such as gout or pseudogout often responds very dramatically.
I had a cortisone injection in my left wrist. But it never did any tihing for the inflamation or the pain. My doctor didn’t give me any more injections because it did not work the frist time. With one injection should I have found some difference or do it take more than one?