The C4 nerve root when compressed causes side of the neck and trap pain which it sounds like are your symptoms. Relief of symptoms with an epidural at that level confirms the pain generation.
Yes, surgery would be helpful to relieve your symptoms. Since the disc is collapsed, an ADR would not be recommended. An ACDF would be the surgery of choice.
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.