Based upon your daughter’s symptoms, one of the more common disorders is a stress fracture of the pars interarticularis (see: https://neckandback.com/conditions/spondylolysis-in-children-healing-potential-and-treatment-pars-interarticularis-fractures-in-the-lumbar-spine-in-adolescents/).
Diagnosis requires an MRI using STIR images so yes, an MRI is necessary. These initially do not show up on X-rays.
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.