Sorry to hear. There are many varieties of labrum tear, and lots of variables to consider whether you go the PT or surgery route. Not sure who you’ve seen, but I think it makes sense to get 2nd opinions (or more), trying to get in with well known sports oriented orthos in your area. Some seem to just put old people back together, some seem to knee-jerk think everything requires surgery, etc. Surgery is a huge commitment, as is long term physical therapy, especially if either wasn’t the ideal option for your situation. Some insurances won’t pay for surgery without a round of PT first though.
I had a torn labrum repaired in 2003, and tore it again last July. The 2nd time around surgery options are different, so I went with PT as I don’t really do anything competitive anymore. It was maybe 3 months before I could touch any weights, and I’m still maybe around 70% where I was last July. I don’t have any nutrition advice, but you’ll want to figure out a bare minimum routine of what you CAN do, and focus on that, no matter how minimal it seems. If you can get a SSB that will go a long ways. After about a month the SSB felt fine on my shoulder, and I think keeping that going kept at least some of the weight loss at bay (I could only load with my left hand though, so it was all 25’s, 10’s, 5’s… looked ridiculous). Come to think of it I did keep the casein shakes going, no idea if that was ideal or did anything but it allowed me to think I was helping something. Best of luck, and let us know more about the labrum tears (size, location, how they happened, etc).