I'm not familiar with a 360° tear in the Labrum but I was diagnosed with what a sports medicine surgeon called a "complete labrum tear"...might be the same thing...not sure.
I second what Switcher said. If you've had an MRI already, you might want to talk to a doc about the necessity of surgery. I hate doing this because I'm always afraid that docs are going to recommend surgery regardless...because money.
When I tore my Labrum (full tear) along with my supraspinatus (partial thickness tear) a few years ago I began guarding my shoulders with my life after I had surgery. I tried rehabbing it but couldn't perform a lot of movements in the gym, suffered a lot of weakness and pain. I personally am glad I got the repair done. I had a fucking arrogant pick of a surgeon but the man was really good and although I have slightly less mobility in that shoulder, it is much stronger than my other one.
Yes, surgery, time off, and rehab post operation sucks...but if it's the only option to continue doing what you love then it's probably better to know sooner rather than later.
I know a few other guys on here have found workarounds for shoulder injuries. One of our members stated that he has a full rotator cuff tear in the supraspinatus, never got it repaired, and he still looks like a damn beast in his late 40's. He found ways to work around this injury and is still going strong.
Maybe there is someone on this board with a similar experience with a labrum tear.
Best of luck brother.