Martina
Try loosening the traps to accommodate, The brace wants to encourage to have good posture, TOS wants us to shorten the path the nerve is being stretched on so we curl or hunch.

I use biofreeze every day, blue ice quilt on the neck head base, and heat on the traps. OR the Relia Med TENS. It is a pulsing massaging feel as opposed to the bee sting type. On the web site they are only $75 dollars.
I hook it up and run for hours.

Deep massage to the traps: use a tennis ball and wall to dig in, get a family member to knead them out, a hot tub.
There is a prescription cream ds uses, it has the baclofen in it....PCP ordered it.

An inexpensive brace is a thin nylon backpack, with a Campbell soup can in it. Just enough to bring back the shoulders.
I did buy a cross the back, lycra back support bra tank for days I have to work.
My recliner is my life during the day, and where I sleep at night.

http://www.medicinenet.com/thoracic_...me/article.htm
It is felt by some researchers that the evolution of the torso of primates from a four-legged to a two-legged position may predispose humans to the development of thoracic outlet syndrome. The resulting vertical posture produced flattening of the chest cage and a shift of the shoulder joint backward, both of which narrowed the thoracic outlet.