TOS is actually a group of disorders that affect either the brachial plexus (group of nerves coming from the spinal cord to supply the arm) or the blood vessels to the nerves, or both. As I have not personally reviewed your case in detail nor have I examined you, I can only tell you about the different types and treatment options for each one. You will have to talk to your doctor to see which one (if any) you fit in and then find the appropriate treatment for you.
According to Dr. Wilbourn, one of the world's experts on the brachial plexus here at the Cleveland Clinic, it can be divided into the following groups:
1.Arterial - caused by large cervical rib or deformed thoracic rib pushing on one of the arteries in the neck/chest area compromising the blood flow. Diagnosed with neck XRay looking at the ribs. Referral to vascular surgeon. Symptoms are on and off. Could possibly be you.
2.Venous-spontaneous clot of the vein in neck/chest. arm becomes swollen and blue suddenly with dilated veins. Diagnosis with vascular studies and referral to vascular surgeon. You do not mention any swelling and blueness, only numb and tingling. Biut then you say abnormal vascular study. Don't know if this is you.
3.True neurologic TOS-Abnormal cervical rib or C7 vertebra with fibrous band compressing the nerve to arm. Wasting and weakness of hand muscles with some sensory loss. Diagnosed with routine neck XRays and EMG. Treatment with surgery. Doesn't sound like you, but possible as I have not reviewed your records in detail.
4.Traumatic-from clavicle abnormality like a fracture with injury to blood vessels or nerves in the area. Diagnosed with XRays of clavicle. Referral to surgeon - orthopedic, vascular or neurosurgeon.
These are the true types of TOS. If you really have one of these syndromes, they will not go away with PT and will likely need surgical intervention. The important thing for you to do is get the right diagnosis as this may not even be TOS. Consider a second opinion at a major academic center. Good luck.