Touching of the spinal cord without significant compression is generally painless. Compression of the cord is generally also painless but the cause of compression can be painful (degenerative disc disease, herniation or painful facet disorders).
Compression of nerve roots will produce pain that starts in the side of the neck, radiates into the shoulder and may radiate down the arm (depending upon the nerve involved).
Spinal cord compression however can cause myelopathy, a generally painless condition that involves muscle incoordination and loss of fine motor skills. See the section on myelopathy to understand that disorder.
Your MRI reading notes only none to minimal cord compression (“The prolapsed discs are slightly touching the spinal cord.”).
You do have compression of the right C5 nerve (‘At C 4/5. there is narrowing of the right nerve root exit foramen with compression on the right nerve root at this level”). This can cause pain to radiate into the shoulder and weakness of the shoulder (lifting the arm).
The C5-6 level also have a disc hernation but this does not cause compression of any nerve roots. This can cause central neck pain however.
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.