It is hard to say if there could be permanent damage. Your job right now is to prevent any further damage while you can find a surgeon to help you. If you do not have a physician to see immediately, at least find a soft cervical collar, the foam type at a local pharmacy. When you put it on, wear it backwards (the velcro fastening in the front-not the back). This will cause some neck flexion (forward bending) which is protective to the spinal cord.
Wear this collar full time (even to bed). Do not try to look up as this action causes neck extension (bending backwards) which can cause further compression of the cord.
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.