I will chime in...probably the minority viewpoint...so take it for whatever it is worth....
I have bilateral TOS..more left than right. Left is the painful side. Nerves, arteries and veins are compressed. Verified by Dr. James Collins, at UCLA.
I have worked with PT and exercise and found help. It is a SLOW process but I am making gains. Less flare ups and less intensity when I do flare up.
In the beginning I had one pain that I sort of played with (this before my dx). I called it "gunk" because it felt like gunk in my left shoulder. It limited my ROM with my left arm and created one of many of my "pains." I did yoga and there was a stretch in yoga called "extended cat dog" which while in Cat you move all the way to child's pose but your arms are stretched out if front. I would often have limited ROM to do this stretch because I'd start and I'd have pain.

I decided one day to play with it and "push through the pain." My instinct told me that perhaps the muscle or whatever "gunk" was knotted up and would release if I did several reps of the extended cat dog. Sure enough it did after about the 3rd to 4th repetition. It was miraculous. Everytime I had this particular pain...I'd do the extended cat dog and voila...it would go away (I still had other pains but at least I was able to do something that would take care of the one in say 5 that I had). Eventually this "gunk" disappeared never to return.
Lately I've felt like I have gunk somewhere else nearby...still left side..but I feel it more when I try to raise my left arm...same idea...limited ROM..pain. Yesterday and today I tried to push through it...I found a reverse sort of windmill and after about 2-3 of those it goes away..of course it seems determined to come back within 5-10 minutes but clearly it does go away such that I can fully extend my arm over head without any other compensating muscles kicking in. I do not seem to flare up afterwards...but it is early and I sense that I will not as a result of this. I can only conclude that YES, at times there is GOOD PAIN that you need to push through to get a release of a muscle contraction/knot/compression.
I certainly will contact my old PT to ask her about it but I'm confident that she will agree to keep doing it if it is not causing any flare ups.
Just my 2 cents.