sometimes you need to totally rest for awhile - but still do some ROM and very gentle stretches and be aware of shoulder/neck postures.
I really feel that finding Sharon Butlers TOS program and even just doing the first 4 things has been a great help for me. I still do those when I feel I need to loosen up.

Then as symptoms ease {hopefully they will} don't be afraid to explore with gentle movement and motions as noname suggests. Exploring and learning what your own body can do is the key.

I had a similar experience with my RSI therapy - got to a point were the forearm pain was constantly @ 2 - PT hooked up a biofeedback unit and my forearm muscles were not fully relaxing. PT suggested some exercises with 1 lb weights for my wrists/arms. slowly to lifting up and lowering and then let my wrist/hand hang over the edge of a table and the weight would help to stretch. It was more sore the next day but as I carefully did more over the next days the deep achy arm pain went away.
But another sx showed up - more of a just under the skin pain - but now I know this is from my version of TOS - the musculocutaneous nerve gets compressed or impinged.

Each of us is so different as to our injury/condition that what helps for one may or may not help someone else.

That's why I think finding a knowledgeable, well rounded and advanced PT, Chiro, body worker, or somebody etc -to help you get a good start on this self exploration is so important.
Hopefully too, they can use some modalities {heat, ultrasound, E stim, low level laser, massage} to help to resolve some of the pain, before getting into too much active uses. so much will depend on communication and how your body responds.

Oh and there are some really interesting and helpful posture, massage, chiropractic- all kinds of therapies you can get a idea about them on the YouTube or Google videos - it is great for an educational tool to see how the good or bad or if it might be something you can do at home that is easy for you.

billy- how did you acquire TOS? from an injury /accident or repetitive type work??