More than one person on these forums has had dizziness caused by TOS. I believe that in at least two of those cases in the last year, people have reported that their doctor (probably vascular MD) told them that their subclavian artery (or arteries) were so backed up that their vertebral arteries had reduced or stopped blood flow as well. This sounds like you.

PT is tricky. Some PTs understand TOS and do good soft tissue work. Most do not.

From what I've read, it's fairly common for people with cervical ribs + ATOS to get the surgery to free up the circulation, plus any scar tissue or fibrous tissues resulting from your injury.

My own dizziness was resolved with highly skilled PT, diazepam for muscle relaxant, posture improvements and time. However, my source is RSI and chronic muscle tension, not injury, and I do not have cervical ribs. You may very well need something different than I needed.

HTH