How long does relief from cortisone injection last before i need another in my wrist?

Varies: It depends on the injury or problem. Sometimes a shot will be a one-time fix. Other times it might only last a short while. I generally don't advocate for repeated steroid shots anyway. For joint issues, I recommend you look up Prolotherapy or Platelet Rich Plasma (PRP). Splints, braces, physical therapy, or supplements such as turmeric, glucosamine, MSM, chondroitin, etc, may also help joints.