Can lower back pain be caused by tetanus shot or could it be tetanus itself?

Uncommon for Td. Just having lower back pain and no other symptoms is uncommon for the tetanus shot and the combined tetanus/whooping cough booster. If it is from the shot, it'll go away on its own.
Neither. Tetanus shot given as DT or Tdap will not cause pain in lower back and just low back pain is unlikely symptom of Tetanus which is serious Disease and takes 2 weeks to 2 months after a contaminated wound in people who have not been immunized against Tetanus Take some pain med or consult your Doctir for low back pain if it persists.