It's pretty common to have ear symptoms with TOS. You can search the forum to get info on that and others experiences. I get the popping and wooshing sensation from time to time. It could be from scalenes or it could also be from the SCM.

As far as surgery, if the doctors said you have compression I would listen to their recommendation. If they are saying surgery it might be your best option. With that being said it depends on how severe the compression is. When I first started I had cold hands a lot and felt like my circulation was very poor. Over time I find that I have less circulation issues. Now most of my issues are pain and tightness of scalenes, SCM, pec minor and scapula muscles.

Thinks to work on - stabilizing scapula if you have that issue.
Breathe with diaphragm, try to consciously do this throughout the day..(this is probably the hardest for me)
Work on posture and back strengthening exercises.
Rest your NECK, every moment of the day we use our neck, take time to lay down, hang your head off a bed, let the neck muscles lengthen and relax.
Self myofascial release with a foam roller helps a lot, I find the lacrosse ball to be helpful as well.
Warm heating pad on your neck can be amazing.

Good luck.