You are asking a medico-legal question of causation. Did the lifting of the toolbox overhead cause a neck disorder? I can’t get into causation on this website as that is a very complicated task.
Unilateral epicondylitis is very unusual from one lifting event and bilateral epicondylitis from one lifting event is extremely rare. Epicondylitis is not associated with hand numbness and bilateral hand numbness should signal the treating physician that there is something else going on.
I assume you have an X-ray that demonstrates significant degenerative changes in the neck. Lifting a heavy toolbox overhead would cause the neck to bend into extension (backwards). If there was significant foraminal stenosis or central stenosis, a nerve or cord injury could result (see website under cervical stenosis and foraminal stenosis). A thorough physical examination by a spine specialist should be able to uncover the diagnosis. An MRI of the neck might be in order.
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.