I would seek a second opinon from someone who removes the cervical rib...especially since my daughters first rib grew back-entirely, and all wonky, and all three of us had pretty much the exact same surgery and have had symptoms return.
Because for me, with surgery-which was somewhat helpful, I also now have new complications-mostly from the missing neck muscle taken with the first rib.
So if I'd had good p.t years ago, instead of bad p.t...then maybe no, I would not have had surgery to have my first rib removed through my armpit.
To be clear, all three of us are thankful for the surgeon who did our resections. At the time, surgery was our best hope. We didn't know any different, didn't know of any options, and it did improve things, somewhat.,.for a while.
The journey with TOS goes on.
Fellow TOSers, Don't hang in there, & Gentle hugs~