After a meningitis shot could i put a cold or hot pack on it for pain?

Yes: I take it that you had a vaccination with menactra, or the Meningococcal vaccine? You can apply a warm or cool pack to the injection site for comfort. This will not affect the efficacy of the vaccine.

Cold: general rule: cold compresses slow down or stop pain messages to the brain. Heat can speed them up. Heat could increase local blood flow and resolve muscle spasm, but the pain issue is helped by cold.