Fern,
Here's a link to a search for vascular docs - just enter your state.
(I checked - there are four in Minneapolis, 1 in St Paul)
If none of them have experience with TOS, at least they are a GOOD link to other Drs who do. Be persistent. I have this condition - it's serious - I'm going to have surgery, but I HAVE to find someone close who has some knowledge and can take over care afterwards. Who would you send your wife or daughter to?
I have found if I leave my name and number with the receptionist, tell her I have TOS and am would like the Dr's advice, even if he doesn't treat it, most will call back. The Dr I finally saw to take care of my infected stitch following pec minor surgery (no local surgeon wanted to touch an out-of-state Dr's work!) was a plastic (hand) surgeon - that's also a possibility you might consider.
Best wishes!
beth