--headache is a well-know post-complication of spinal tap, but, if the headache persists beyond a day or so, one should be talking with one's physician; there are cases in which the opening through which spinal fluid was drawn doesn't close up completely, resulting in a spinal fluid leak which can cause persistent headache as the spinal fluid concentration around the brain is less than optimal.

In a situation like that, a blood patch or other alleviating therapy may well be called for.