Very high arches can cause you to alter your gait, which can result in back pain. With high arches, the feet tend to supinate, or roll out. This results in the ligaments and skeletal structure exerting an external rotational force on the tibia & fibula, which continues at the knee joint, femur, pelvis, and possibly even the spine.
If your back pain is the result of high arches, my recommendation is to see an Orthopaedic physician who specializes in Sports Medicine. They may refer you to a Physical Therapist or someone like myself, an Orthotist. An Orthotist can fit almost any brace on the body, from the head to the foot, excluding the teeth. If the plan includes seeing an orthotist, it most likely is because the doctor has written a prescription for a pair of custom foot orthotics. For someone with high arches, the orthotics would most likely include a lateral post, along with an arch support that is fabricated to your specific arch. The goal of the lateral post is to reduce the amount your foot supinates, while the arch support allows limited flexibility. The flexibility reduces the shock that the ground reflects back to your foot as it moves through the gait cycle. The reduced movement that the custom arch support and lateral post provide helps restrict the excessive rotating of the skeletal structure and connecting joints from the foot through the spine.
Back pain can be the result of many variables, however, the best way to determine what is causing your back pain is with the help of an Orthopaedic physician who specializes in Sports Medicine, and possibly a physical therapist. They are best suited to help you determine the cause(s) of your back pain.