The lower prominent vertebra you feel (I assume from the back of the neck) is C7 called the “vertebra prominens” in Latin as this is the most prominent spinous process noted.
Pushing on this spinous process should not shift the spine too much to cause compression of the cord. I am unsure why you develop these symptoms.
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.