4 lumbar facet injection 4 weeks ago. no pain in this area prior. now have soreness in area of injection in center lower back, is this normal?

Low back pain : Yes. Sometimes the injections can irritate the nerves, muscles and joints. Try moist heat and stretching the back in the morning. Apply ice to the back at night. A low profile back brace may help relieve the pain too. If the pain persists then see a neurosurgeon.

Facet Treatments: Its normal everyone is different with the facet injections. If those provide relief but short-lived would recommend medial branch block radiofrequency ablation for more longer lasting relief.