Is it okay to have terrible stinging pain after lumbar puncture (spinal tap)?

Yes. The lumbar puncture procedure can cause some local back pain. The back pain should not last for more than 2-3 days after the procedure. It should not cause severe back pain. Talk to your doctor if you develop any headaches, numbness/tingling/weakness in the low extremities, severe back pain, or any difficulty with bowel or bladder function.
Occasionally, one . Can experience pain at the tap site for a day or two. If it is radiating down a leg it means a nerve may have been irritated.