First off, I'm not a doctor, nor did I stay at a holiday in recently. However, my gut instinct is that you might be shrugging your shoulders up in your jerk and pushing them down during your press. That shrugged position (where you're neck disappears) might give you issues if you've got tight scalenes or other stuff going on. Beyond that, I'd go see a real doctor.
Can you post a video of your jerk, push press, and press?