I'm sure if the docs thought a MRI was needed they would have done that.

Have you had any basic neck/c spine xrays during this time?
Just to make sure there are no bony anomalies? like extra cervical rib? large transverse process?

The past shoulder pain/injury could have caused some internal scar tissue.
I had chronic shoulder pain for a long time then wrist pain then it spread to the elbow , whole arm upper back/neck...

wet/damp weather and weather changes will tend to make more pain..

If those things you are doing for pain are not enough, then it is time for a doc to rx meds.

The venogram will show where the problem is , if it is vascular related or not.
It sounds like this is something that needs to be done..also in case surgery becomes an option , it probably is required as dx proof.

Much of TOS dx is ruling out of any other causes.

Being posture aware is good, esp if shoulders/head are forward of the body, getting them back to aligned gently should be a good plan.

For some with VTOS the overly military posture increases sx so be aware of that if you do posture work.