Ada,
How did the right side TOS surgery work for you?
I haven't had it done, but have a nasty case of TOS. My docs (Schwartzman and Hunter),
told me that the sheath muscles "the ones that cover the back of your shoulders, and shoulder bone) would naturally atrophy. And, they did! It took well over a decade, now I can feel my shoulder bones (sorry for not using medical terms) just by reaching over with my opposite hand. They can also been seen, (through my skin of course) with my shirt off. That wasn't the case when I was first injured.

I have a good friend who's had the rib section, and she says it helped, but she and I still have great difficulty with TOS.
On THAT basis, I would say don't expect a cure, but perhaps some help, because so much of TOS is the scar tissue that remains from the original injury, and surgery can cause more. This causes an "abrasion" of the nervous and vascular systems upon movement.

It's personal preference, and I wish for you the best outcome!

Pete