I think muscle relaxants work on the nervous system as well, right? They are not drugs for the muscle tissue, but drugs for the nerves that stimulate the muscles to tense.

Regarding TOS nerve pain, it's caused by compression that is caused either directly by muscles or by muscles pulling on bones (first rib and collar bone). Anything that can safely reduce that tension is often helpful to TOS.

I do have to warn that if you just kill the pain without relaxing the muscles and/or adjusting the bones, then the irritation to your nerves may continue which could make things worse over time. Sorry if I sound like a downer, but I think it's a real concern and had to share it.