Should there be pain in spine after a local anesthesia block there?

Should get better! Any time a needle is inserted, it will cause some tenderness and bruising. There is an inflammatory response because the body interprets the needle stick as an injury. Try a heating pad, gentle stretching exercises, and a nonsteroidal pain reliever such as Ibuprofen if your doctor oks it and you have no contraindication such as kidney problems. It should feel better soon!
Yes. As you can imagine the back and muscles do not appreciate having a steel needle passed through them for a pain block. This means that they can be in spasm or are bruised after the block. This can last for a few days to a couple of weeks. It will get better on its own, but it is disconcerting. I hope that this answers your question.
Confusing. A local anesthetic block in the spine? Not clear what you mean. A spinal anesthetic (local anesthetic into spinal fluid) can rarely cause headache after. Injection of local anesthetic into the skin should have no residual effects like that. Rarely either injection can cause a bruise which can be very tender.