Could be a strain, or pinched nerve. Probably benefit from a course of P.T. Make sure to find a Therapist that's well experienced with neck problems, because they can be a little tricky.
My suggestion is to have a cervical spine MRI to see if there is an impingement on some of the nerves.
I have a condition that causes the cartilage in all my joints to be eaten away and it has caused me some of the same kinds of stiffness and a feeling that the neck doesn't want to move. When I do get my neck to turn, it snaps, audibly and then everything loosens up and I'm all right again.
I doubt you have what I have, but I use it to call attention to what you are talking about and the fact that an MRI for me, shows impingement of nerves in the neck.
This MIGHT be the problem!
Whatever you do, don't wait! Get it checked out to be sure that leaving it alone will not cause more damage if that is what is actually occurring!
Best of luck