A labrum tear can cause what you’re probably describing as your shoulder subluxing (partially dislocating and then going back in).
A labrum tear generally won’t heal on it’s own since cartilage doesn’t really get any blood supply and if that is what it is, constant subluxing can make the tear worse. Your doc will probably start your with PT, it’ll suck but if it works, it’ll help you build up the muscles around the area to support the your shoulder where your labrum is failing.
You can look around at the various tests for labrum tears. There’s a bunch of different types of tears, but all the names (SLAP, Bankart, Posterior Bankart etc) really just have to do with where the labrum tore, what the tear looks like and how bad it is.
SLAP tears, BTW, you need to be careful with since that directly involves your bicep.
You can find all the various tests your GP/ortho will do and but IME, you really can’t replicate them at home. I tried, but I’m sure it was just a combination of not know what I was doing and not being able to bend my own arm into the correct position. I would sit there and read the diagnosis stuff online, try it and get nothing. Walked into my doc’s office, he said 'hold your arm like this’, he (lightly) torqued on it a little and I stood up and walked with him (imagine someone pulling on your hair) to get the pressure off of it and said (‘yow, jesus fuck’) as he collapsed in his chair laughing and said ‘yup, you tore your labrum’. I already knew it going in there based on my symptoms.
Also, you said it came on suddenly, I assume you don’t recall any kind of trauma or injury, right? You didn’t fall on it? Run in to something or break a fall with a stiff/outstretched arm? Hit or fall on your elbow? Basically do anything to your shoulder?
When I tore mine I knew I did it, I heard the pop. It wasn’t horribly painful or anything, but the pain just never subsided. If you didn’t actually do anything, it could be something else, or could still be a torn labrum that was just recently inflamed or exasperated**.
**I read somewhere along the line that many people go a long time not know their labrum is torn. So many people, in fact, that if it’s picked up on a scan while looking for something else and the patient hasn’t complained about it, they’re no longer fixing it ‘just because’. So you might have had it for months or years and a few weeks ago bumped it or slept funny or played an extra rough game of tennis or helped someone move and now you’re noticing it. Which gives me another thought. Look up “shoulder impingement”. Especially if you have pain while moving your arm through the upper few degrees of motion (like reaching over your head).
I can second asking for recommendations. I to had an NBA/MLB guy, he’s apparently the ‘Shoulder God’ around here, an easy way to get recommendations is to watch for people in slings and ask them. You have plenty of time right now, you can start by just looking at slings and seeing which brand you see the most and start there. You could even call some of the physical therapy places and ask them.