Hi, you need find out what causing your thoracic outlet, ie tight scalenei in which case you must stretch these, a 1st rib in which you could mobilise this. But one piece of evidence for thoracic outlet syndrome suggests that a progressive strengtheing programme of shoulder elevation is proven to alleviate the pain.
Roughly...
Week 1. Do sets of 10 shoulder elevations 10 times a day
Week 2. Same again with 1-2 lb weight in hand.
and so on, increasing the resistance.

Good luck.