Hi,
Do the veins and /or arteries them selves seem to swell when the arm gets red like that?
I would say the arteries are getting blocked /pooling?? and that's why it gets so red instead of the pale white of loss of pulse. just guessing a really good PT should be able to pin it down.
Or possible RSD, if skin gets blotchy, and mottled and hyper sensitive to touch and such.

Mine only go whitish when raised and then reddish as the blood flow returns when they are lowered.

Do you have an idea of how your TOS came about?
RSI , fall or accident, car accident/whiplash..etc?

""Tourniquet" feeling around my left bicep/triceps area" yes quite a few have mentioned that, mine rarely flares up anymore.

Testing -
I think they are hesitant to rx many tests when pain & symptoms are mild, moderate and intermittent . (no rx pain meds being used.)

Which I feel is a good thing for you, if you're sure there are no c spine causes for the pain /sx and the other basic possibles are ruled out -then proper PT with advanced therapists or an expert chiropractor along with self care and posture awareness, you should be able to turn it around.

It isn't a quickie fix , it will still take time and learning to read your body.

Some of my sx & pain levels were somewhat similar, I was taking advil/motrin at the time, although it was over the suggested dosages when i was still trying to stay at work. (3 months = too long to take it)
I only used vicodin a few times during the severe spasms to get some sleep.

Once off work i stopped that stuff - as I read it does inhibit cellular healing after a time and it had affected my tummy/gut a bit.

All in all it took me about 2.5 yrs to get it under control.
I still go to a good chiro fairly regularly - if Ii miss more than 2 months I can begin to feel it all over.