I love shoulder problems like this, but recognise that not every chiropractor treats extremities. Some chiros only work on the spine.
But your shoulder problem is certainly connected to your neck. Both ways. It may the result of a neck problem, or it may be causing a neck problem. Does your lower neck hurt?
The first rib is critical to this problem. A fixation of the first rib can profoundly affect the brachial plexsus, the subclavian artery and occasionally vein. It's known as a Thoracic Outlet Syndrome.
Anyway, before you EVER go for surgery try the conservative thing first. Try the Frozen Shoulder exercises at C-H for example. Visit a local chiro who works with shoulders, do your homework first.
Not having examined you, I can't promise anything, but I suspect you have a problem that can be greatly helped with Chiropractic.
Let us know how you get on.