I recently added iron supplement. They say iron is necessary for oxygen levels in the blood. I think I've been getting enough iron, as a vegetarian, but on a talk show, they said to push down the skin below your eye. If that area below your eyeball is red, you are A OK. If that area is white, you are low on iron. Well, mine was really white.
Stuns me, although a talk show is not accurate science, because I had blood work done that measured hemoglobin (a test for iron I understand), and it was fine.

So, could iron deficiency cause TOS? Ugh. hahahahahaha.
I know they say it can affect nerves.

No.