Your description of a “slight disc hernation” at C6-7 does not fit with the pain and motor weakness that you describe. I assume that there is a substantial herniation or something else is causing these symptoms (Parsonage Turner syndrome or the like).
Shoulder muscle contraction is typically related to disc herniations but there are many other disorders that can cause these contractions. I am concerned that the physical therapist found significant muscle weakness of the trapezius. When you note decreased strength with workouts “I attempt to do very light workouts, it aggravates it and I lose some strength in my left arm again”, this is an indication that the strength in the arm is still significantly poor. A muscle that has lost much of its nerve supply may seem strong initially but will fatigue quickly.
Grip strength involves the C8 nerve which is not involved here. Measuring grip strength will not indicate anything about the health of the C7 nerve. I am unclear about; “other strength tests by my chiropractor show that neighboring discs are also affected” as this would be unlikely.
You need to find a well qualified, meticulous and experienced spine surgeon to give you an opinion. Bring all your studies with you to that visit.
Dr. Corenman
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.