Well...
What you describe could be several things, but it sounds suspiciously like a problem in the AC (acromio-clavicular) joint.
One thing you might want to try and determine is this:
In the past week or so that this has bothered you, has it improved any?
Soft tissue like muscle will improve at least some, and will feel worse after use or later in the day.
Connective tissue stuff, like strained tendons and ligaments, tend to be very stiff and uncomfortable when you first get up, but feel better as you use them a bit.
If this hasn't improved at all that you can tell, I'd get it checked.
Hope you're feeling better soon!