From what I gather, as long as your doctor feels that you are actively trying to get better but your condition hasn't improved enough to go back to work, you are entitled to workers comp for a certain amount of time.
Welcome - Tennessee Department of Labor and Workforce Development
If you scroll down a bit there, you can see the amounts of time you are allowed to collect workers comp for various types of injuries. It doesn't specify wrist, but I imagine you would be somewhere between 150-200 weeks.
After that time, I'm not sure what happens. I think you if you're not healed by then, you would get offered a cash settlement or possibly continue workers comp if your doctor feels you're close to recovery.
I can't imagine a wrist injury is going to take 3 years to heal though.
Bottom line: You should contact a lawyer. Unless there are other circumstances you haven't mentioned, it sounds like you have a pretty clear case even without them making you wait to go to the ER.
