I think if it is clearly a vein or artery compression causing most of the trouble , there is a better chance of a good recovery, with a very good surgeon of course.
Nerves are trickier as they complain much longer even with a successful surgery.

Your computer use & swimming are kind of a double whammy for possible ongoing issues, even if surgery is totally successful.
Certain activities & postures can aggravate the same scenario that caused the problem of TOS in the first place..
It might be wise to look for other less arm/shoulder based activities /sports for fun and fitness.