The biceps tendon attaches to the labrum so pretty much anything you do with your arm is gonna aggravate it. When they opened mine up the tendon was so frayed that he just cut it and reattached it to the humerus.
An ortho is probably going to tell you to get a MRI, but it's still hard to tell even from that. The only way they're really going to know is to scope it (in surgery).
If it truly is a labral tear, the only solution is surgery. I had done it last November and my shoulder's 100% now. (I don't do kipping pull ups or muscle ups anymore)