Yup, that certainly sounds like Thoracic Outlet Syndrome. But I also wonder, given some of the other info you've posted, if you've having additional neurologic trouble from other causes.
There is a concept in neurology known as the "double crush phenomenon"--when peripheral nerves are assaulted, they may or may not be symptomatic, but when they are assaulted by more than one condtion, previously minor symptoms may blow up, or symptoms may appear when they did not before.
This has been well documented, for instance, with diabetics--because their nerves are often already suffering ischmic damage, they are more prone to compressive effects than non-diabetics would be, and so have higher rates of carpal tunnel, tarsal tunnel, and spinal nerve root compression (radiculopathy). This is also common in people with hypothyroidism and autoimmune conditions; it seems the second hit is what really makes symptoms increase.
You may want to get a more thorough neuro work-up to check on such possibilities (especially ulnar neuropathy, with those hand symptoms). Many of us like (and contributed to) the spreadsheets at
www.lizajane.org; great way to see what tests you've had and track results over time.
Two other good links here--
The peripheral neuropathy forum:
http://neurotalk.psychcentral.com/forum20.html
and the thoracic outlet forum:
http://neurotalk.psychcentral.com/forum24.html