What symptoms suggest back injury?

Depends. Depends on the severity of the injury bachache, radicular pain if a nerve is pinched all the way up to the bladder and bowl symptoms. There is no spinal cord at the lower back level, only nerve roots but higher up can cause spinal cord problems with important sensory and motor symptoms.
Painfultightness. Most injuries of back are simple muscle strain resolve in2-4months regadfless of treatment.
Some obvious. Obviously, localized back pain would suggest problems of the back. Stiffness of the back particularly in the mornings would be a consideration. Some people with back problems may not have specific back pain but rather tingling, numbness, weakness, or pain down a leg which suggests nerve irritation coming from the back, which is still a back problem.