How might I cure a back injury from tennis?

Find out the cause. Most back injuries are the result of repetitive stresses. Weak core muscles and muscle inbalances of the lower extremities can cause abnormal movement patterns and contribute to recurrent injury. Consider an evaluation by a sports minded practictioner to help you get back on track.
Get checked . First. Get checked for disc problem then nsaids and physical therapy, resting and ice tend to help.