I had something that sounds real similar to this. It came on suddenly, and nearly put me out. I tilted my head to hold my phone to my shoulder so I could write something down, and when I moved back to normal, this thing got me. Something that seemed simple enough, but I ended up going to the ER I couldn't sit for long, it hurt to breathe.
They loaded me up on pain pills and sent me to physical therapy to try and work it out. Eventually it got better, but I still feel a twinge and it's been months. They said it was a pinched muscle, I tried the chiropractor, but he couldn't get to it, and I could barely stand to lay on the table. I had also damaged my rotator cuff before this happened, no idea if that contributed to it in any way, but who knows.
Definitely see a doc though, they will be able to get you the right therapy to straighten it out.