If it were me I would keep going to PT. It takes a long time, work and some pain to unfreeze a shoulder. Many people think the best thing to do is leave it alone but that is what causes it to freeze. Your body is covered with fascia and that is what needs to be made more pliable. Your PT will make sure your shoulder is properly in the socket and should give you exercises to help. If need be you can get another PT. (If it's been many years that your shoulder has been frozen then it may be impossible to completely unfreeze it but you still could probably get some more mobility)

As far as an injection that would probably help with the pain. Do you have a lot of pain? If not I would ask the PT if it would be helpful or harmful in unlocking a shoulder.

I try not to give up on any of my body parts unless I really have to, but that's me.