I have had only scalenectomy for subclavian artery compression with exactly same symptoms as yours and I am doing great on right side(2002). I was also perfect on left side after scalenectomy (2010) till scar tissue built up after 10 months post surgery and I am working on PT exercises and really good manual PT is helping me. Good news is that it is easier to fix the vascular issues than the neural issues, because the arterial compression shows in the fallout in the subclavian artery in the MRA and/or Doppler ultrasound and they can see it quite clearly. You might have bands compressing your subclavian artery. (Bands are however hard to see in imaging till the surgeon goes in.)Has to be done by a good vascular surgeon who does quite a few of these. They usually do an MRA after surgery too to see if the blood is flowing properly before they close you up.
I did months of PT before the surgeries but PT was not helping me. I am so glad I had those surgeries, because too much compression can lead to an aneurysm in the artery if it is serious compression. Sorry I am not trying to scare you. Please get a second opinion if you can and then decide.