There's been some great advice thrown out for you. To decide on surgery or no surgery is tough. The question is: how much of the labrum is actually torn? The results state "antero-inferior to postero-superior" but this is pretty vague. You want to get a clock position tear description. This will give you a better sense as to how much of the labrum is torn. Your current pain levels, description, and behavior will also guide you. Are you in tremendous pain with very little movement? Or can you be pretty active before flaring it up?
The conservative approach is physical therapy. You may be able to drive your pain levels down with increased strength and functionality, depending on where you are at now. If you get better, you can avoid surgery at least for the short run. Much will depend on what you do after therapy is done and how consistent you are with home exercises.
Someone also mentioned having your acromial space checked out. Since that supraspinatus runs under the AC, there might be a "hook" in the acromion causing the tear. If no hook, the tear might be a result of an impingement caused by para-scapular muscle imbalances, usually lower trapezius weakness, along with others (rotator cuff muscles for stabilization).
What does your doctor suggest? If they suggest therapy, I would recommend you do this even if you decide to do surgery. If there are muscles weaknesses that can improve, this will help to drive better outcomes after surgery.
This is just a bit of information...I hope it helps.
Mark
Physical Therapist
Mark Payares, PT, DPT, CSCS
Physical Therapist
USA Cycling Coach Level 3
http://www.start2finishstudio.com