Definitely go back to the hospital. I had a post LP headache after a lumbar puncture for suspected meningitis about 10 years ago (turned out to be just a throat infection). I never left hospital as I couldn't get to the toilet and back without vomiting and crushing headache. I couldn't even sit up to feed myself.

They often resolve by themselves after a few days of bed rest but if it's not settling they can do something called a blood patch to fix it. They basically take some of your own blood and inject it at the puncture site where it clots and seals the hole. This fixed mine but in hindsight I should never have let the doctors wait a whole week before doing this!