Seek out a TOS specialist or a skilled vascular surgeon, that has done cervical rib removals.. Don't waste time seeing Drs that do not understand or know about TOS.

The choking part could be from the C ribs , or your 1st rib might be raised up and impacting /crowding your throat even more.. I had that problem without any c ribs..
A very skilled PT guy did a rib mobilization /rib drop technique and it was instant relief..my 1st rib had got raised from severe spasms and got stuck in the raised position.. it really limited my arm use too. After the rib dropped down I was able to drive home without changing arms /positions, and do chores at home without increased symptoms..
So you might benefit from an expert PT or expert chiropractor..especially if they use additional tools and a mix of therapies..
My chiro used ultrasound, trigger point, massage, IF stim, low level laser..also checked overall posture & for uneven shoulders, hips etc...
It must be someone that assesses you each time and does not use a set plan - a set PT plan rarely work as weights, hand bikes and such often make TOS much worse..

Try to be posture aware so shoulders aren't forward, hunched and closing the area more, you might have to experiment to find best posture for you..
Often kids can get by with C ribs for awhile, but as an adult with work/ repetitive jobs, add in any injuries, those ribs can rub inside the body making internal scarring..
Those things might be adding to you issues now..

That is why you need a skilled & expert surgeon, it sounds like your nerve is getting affected as much as the blood or or maybe more than blood flow.
If you mentioned swelling, color changes & possible clots , then VTOS would be the main concern. The longer a nerve is compressed it will take longer for it to come back, and there may be lingering pain ..

Check out our sticky threads in the upper part of the TOS forum main page.
Drs/PTs, useful info, Trigger point etc..