Sore back after falling and hitting head running backward on tennis court?

Not Uncommon. Obviously age, previous back problems or other musculoskeletal problems could make the fall more serious. Doubt fracture of the spine unless pain excruciatating. Most likely muscle sprain/strain/bruise. Also head injury needs to be watched for. Watch for any headaches, vision changes, nausea or vomitting, or any other neurological complaints. You may need to be looked at by physician.