In theory, yes, you could have surgery to repair (probably reconstruct) that bum shoulder. But in reality, you’ll need to have an orthopedic surgeon evaluate your arm in order to answer that question for you. The standard treatment for recurrent shoulder dislocation is to reattach torn muscles and smooth or repair the labrum if it has frayed or pulled away from the bone.
The labrum is a fibrous rim of cartilage around the shoulder socket. It helps give the socket greater depth in order to stabilize the round head of the humerus (upper arm bone) in the shallow acetabulum (socket). With repeated shoulder dislocations, there’s a pretty good chance you have some involvement of the labrum that will need attention.
Most surgeries of this type are done with an open incision but a recent study from Italy showed good long-term results when done arthrocopically. By inserting a scope through several small openings, the surgeon can avoid cutting into the muscles around the shoulder. Even in patients who had a 10 to 20 year history of recurrent shoulder dislocations, there were successful results.
The big concern with long-term shoulder instability such as you describe is really arthritis. A loose, unstable joint doesn’t have normal biomechanics and smooth movement. Those two factors are enough to cause uneven wear and tear on the joint resulting in degenerative arthritis over time. Surgery to repair the instability can (and often does) reduce the risk of progressive arthritis. If for no other reason, you would be advised to seek the counsel of an orthopedic surgeon…and good luck!