Thoracic outlet syndrome (TOS) is not related to neck origins or instability. Read the section on thoracic outlet syndrome on this website to understand the pathology.
Instability of C1-2 can cause base of the skull pain and headaches but not tinnitis or “tingling lips and tongue”. Instability of C1-2 can cause dizziness.
You cannot determine hypermobility or instability without motion X-rays or a CT scan with the head placed in different positions.
First- work with a therapist who is expert in TOS. You can try brachial plexus injections if this is ineffective. Finally, if nothing else works and symptoms are unacceptable, a surgery to release the thoracic outlet can be effective. I do not do this surgery.
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.