After a spinal tap is it normal to have stinging pains lower than the puncture site on one side of your back?

Yes: Many people with lumbar punctures have persistent pain around the puncture site for quite some time. The stinging pain may simply be lumbar spasms as well. If they persist, see your family dr. For evaluation and treatment options. If there's any redness or swelling, see your family dr. Right away.

Yes but improving?: Yes it is occasionally not alto experience minor numbing and tingling sensations following a spinal tap but it should be improving and not worsening in which case you should emergency contact your physician.

Perhaps: Any stinging in this manner should be from irritated nerve bundles (distal) outside the spinal fluid enclosure that would carry pain/temperature fibers. Thus the symptoms should subside in a few hours or 2-3 days at most.