The problem starts here. For starters, there are at least two
TOSs: both rare, one drastically overdiagnosed.

There is vascular TOS, in which the subclavian artery under the
shoulder is partially occluded by a cervical rib or fibrous
band. There upper limb is pulseless and gangrene can develop.
It needs to be distinguished from Raynaud's and from
atheroscl{*filter*} disease of the subclavian artery. Surgery
relieves the problem.

There is neurogenic TOS, in which there is chronic compression
of the lower trunk or medial cord of the brachial plexus by a
cervical rib or fibrous band. The hand atrophies and becomes
very weak, both on the thumb side (median nerve) and pinky side
(ulnar nerve). There is numbness of the pinky and that border
of the hand and forearm - but don't count on that symptom,
because it is also produced by ulnar neuropathy at the elbow
and by C-8 radiculopathy in the neck, conditions that are about
100x as common as neurogenic TOS. This condition is *rare*,
estimated at 1 per million of "true" cases. It is also way
overdiagnosed by unscrupulous surgeons. Surgical results are
iffy even in "true" cases.