The term "tear" can also be misleading itself.
The labrum is a thick piece of cartilage or cartilage-like material. It is supposed to be affixed to bone at either end.
It can tear within itself, the way you think of a sheet of paper tearing.
It can also just detach from the bone, without suffering any damage to itself. That is also commonly referred to as a "tear".
In really bad cases, you see both things happening. Some extreme cases have the "fraying rope" issue where medically it's just hard to put the pieces back together.
There's no way your son could've continued throwing and lifting if he had that worst case scenario. The pain would be terrible and also the loss of function would be noticeable.
One thing you don't say is whether your son has seen a loss of velocity. That is also a sign of how severe an injury might be. If he had that, I would think you would've mentioned it. That makes me think you have reason to hope that things are not too bad for your son, and that maybe he has the pitcher's lament, laxity in the shoulder capsule. That is a rehab issue, not a surgical issue. Laxity is literally an overstretching of the shoulder capsule muscles, which is treated with throwing rest, toning exercises and then a forever conditioning program (which really all pitchers should be doing anyway, but they wait until they have an injury to find that out the hard way).
What bothers me is that you have missed 6 months of opportunity to shut down and then work the rehab program. I guess if he's not yet HS age, you aren't worried about HS tryouts yet (which start here in about 8 weeks), but you need to get on this NOW so that when his favorite time of year gets here he can hope to be healthy and ready to go without any second thoughts -- if it turns out it's just something he needs to rehab and not a surgical case. If he keeps trying to push through this without the proper approach, this problem could force him to lose an entire spring/summer season.