I just looked at the first C/J video you posted. The first thing I notice is the bar path looks like its pretty far in front of you. Per Greg, "aim for the back of your neck when Jerking." As you start to drive, you should move your head back so the bar can go straight up, and should never be in front of your base of support. Fix that and see if you have any more pain.
Also, it does look like you are shrugging. You sort of do the turtle shell thing when you jerk. Retract your shoulder blades into the girdle and keep them there throughout the movement. You can practice this during the press and spend a bit of time at the top with your shoulders down to ingrain this position.
Third, do all the mobility stuff that Greg said. You'll be better off in more ways than you can imagine by loosening that stuff up.
Best of luck!
PS. where are you lifting at?