I just had a spinal tap in Octber and my back was sore at the site for a couple of days, but I have no lingering pain from it. I also had an epidural with my son, not to mention many nerve blocks higher up because of shingles.
I don't have any back problems as a result of any of them.
Check with your doctor. Your back pain could be caused by something else. I know that my chiropractor really helped me. My back was out of whack from my body trying to compensate from the weight of the baby and then adjust back after he was born.
Just a suggestion.
I'm sure your baby will be just fine.
Best wishes.