how long after back accident do i have to file a claim

You don't say how you injured your back, whether it was an auto accident, medical malpractice, a slip and fall, etc.  Regardless of how you sustained the injury, however, in Tennessee, the Statute of Limitations, or the amount of time you have to file a lawsuit, is one year from the date of the injury.  If you are approaching the one year point, I would encourage you to contact an attorney who can file suit immediately on your behalf to protect your interests.  If, however, you have ample time, if your injury is not severe, you can consider filing an insurance claim with the insurer for the responsible party.