I have a mate who can pop his shoulder in and out at will, very strange,
Me on the other hand... Took a heavy fall on my shoulder and dislocated it, once it happens once its very likely to happen again, and again. I got physio too but by the time i was referred to a physio it was too late, i'd dislocated it again and the damage was done, i had to have surgery in the end.
The physio helps as it builds up the muscles around the joint which then help to hold it in place, if it worked for you, might be an idea to do some of the exercises on your own.
It doesn't sound to me as if your shoulder is fully dislocating, the uneasy feeling is a reaction of the body to try and stop you putting your shoulder in a vulnerable position, most vulnerable is with the arm raised, upper arm extending sideways level with shoulders, forearm pointing upwards at 90 degrees, the kind of position you get to in climbing a lot i imagine.
I'm not a physio or surgeon, but from what i learned with my shoulder, ligaments do not repair themselves, if you cant live with it you have 2 options, do strengthening exercises or have surgery. Obviously exercises is the place to start, unfortunately it didn't work in my case, although if i'd have understood more at the time i'd definitely have worked a lot harder on them.
Surgery sounds pretty drastic, but i knew it was time when it popped out waving at someone! On the plus side, 3 years on my shoulder feels better than it did since dislocating, and i am confident in using it, towards the end i was barely using my left arm because of the fear/uneasy feeling.