Arachnoiditis can cause local pain but typically causes leg symptoms and many times arachnoiditis is an incidental finding (not generating symptoms). Rhizotomies and facet injections would treat lower back pain (LBP) generated by the facets which has nothing to do with arachnoiditis. This assumes that your LBP is the only symptom and is only facet generated (not typical).
I would start over with a new spine surgeon and obtain new imaging studies (MRI) as you might have something undiagnosed yet to treat.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.