I had a spinal tap during my diagnosis. The actual procedure was not painful although I did feel a slight sting as the needle went through the skin. I was told to stay horizontal afterwards. However, I was stubborn and told the nurse that I felt fine. I showered and then had dinner in the hospital cafeteria. Halfway through my dinner I started getting really nauseous from the headache and had to go lie down. The headache stuck around for about 5 days and I had to go back to the hospital to get a blood patch. It sounds like your doctor wants you to do a lot of walking around after your tap. Getting an MRI should not be a problem as you'll be horizontal, though I would make sure that the wheel you there on a gurney and that you not walk around. My MRIs would typically last for about 30 - 45 minutes. However, I would try staying horizontal for about an hour or two in total.
Another factor is the needle bevel orientation. The fibers of the dura are oriented longitudinally. Thus, if the needle bevel is perpendicular to the fibers, then it tends to cut them and do more damage creating a higher likelihood that there will be a prolonged fluid leak at the puncture site. However, if the needle bevel is parallel to the longitudinal fibers, the damage at the puncture site will be less and hopefully there will be less problems with fluid leaking from the puncture site.
It might be a good idea to read this thread
first and make sure that the doctor doing the tap is aware of the issue raised by jimmyleggs concerning the needle bevel orientation.
Needle bevel direction and headache after inadvertent dural puncture.
Norris MC, Leighton BL, DeSimone CA.
Department of Anesthesiology, Thomas Jefferson University, Philadelphia, Pennsylvania.Anesthesiology. 1989 May;70(5):729-31.
To study the effect of needle bevel direction on the incidence and severity of headache following inadvertent dural puncture occurring during the identification of the epidural space, the authors randomly assigned obstetric anesthesia residents to identify epidural space with the bevel of the epidural needle oriented either parallel or perpendicular to the longitudinal dural fibers. If dural puncture occurred, an observer unaware of the needle bevel direction, daily assessed the presence and severity of any subsequent headache. Of the 1,558 women who received epidural analgesia during this study, 41 women suffered dural puncture, 20 with the needle bevel oriented perpendicular to the longitudinal dural fibers and 21 with the needle bevel inserted parallel to the dural fibers (NS). Fourteen of 20 women in the group in which the needle bevel was perpendicular to dural fibers developed a moderate to severe headache, whereas only five of 21 in the group in which the needle bevel was parallel to dural fibers did so (P less than 0.005).
Similarly, we administered a therapeutic blood patch to ten of 20 women in the perpendicular group but to only four of 21 in the parallel group (P less than 0.05). Thus, identifying the epidural space with the needle bevel oriented parallel to the longitudinal dural fibers limits the size of the subsequent dural tear and, therefore, lowers the incidence of headache should dural perforation occur