Is it okay to have lower back pain after a tetanus or meningitis shot?

Not really. Did you get the shot in your buttock? If so, this can sometimes result in irritation to the sciatic nerve, or you can develop a tender point in the gluteus muscles. Best to contact the office where you received the shot and inform then and ask for advice.
Probably unrelated . The back pain is probably unrelated as this type of pain is not uncommon to begin with as up to 85% of people will experience this type of pain in their lifetime. If the injection was in the buttock region, this could cause a local inflammation fairly immediately that could present like back pain but should resolve just as quickly.

Related Questions

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. Read more...
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. Read more...

I just got a tetanus, chicken pox, and meningitis shot today. Is it normal for my whole body to be aching? How long should it last?

Yes. Immunizations can have side effects like the ones you are experiencing. They normally go away after a day or two. Read more...
Multiple immunizatio. It is common after having multiple immunizations to have generalized body aches. This should subside after several days. Read more...