A few have had C spine /disk problems along with TOS.
What level was your disk herniations at? C 4 /C 5/ C 6 or C 7?

What kind of treatment did the dr suggest?

If some gentle , basic PT is rx'd that should be OK either way as long as you tell them if anything begins hurting worse.
And some easy basic posture work shouldn't hurt and may help.

in our useful sticky we have some posts with illustrations of the nerve routes from the c spine- you can see if your disk injury matches up with any hand/arm pain you might be having.
http://neurotalk.psychcentral.com/thread84.html
post 1 has anatomy links and post 15 has some pictures