Judging by the handlebar pictures and stem it looks like you are too crammed inside the frame . Looks like you may tilt the handlebar forward a little so the bar ends point to rear brake caliper (should be between the seat clamp and rear drop out), then adjust the shifters. Looks like brakes/shifters should go forward and the bar should come up. Even if the bike will be set up correctly it still does not guarantee that you will not have neck issues.
I recommend looking to the saddle height and tilt(very important) positions . If the tilt of the saddle is not correct you will push with your hands on the bars, locking elbows at times and causing neck/shoulder pain. Try to set up your saddle even or slightly nose up and see how it is.
Once you figure out the bar and saddle position I would pay attention how you sit on the bike, make sure you do not have a death grip on the bars and shoulders are relaxed and elbows not locked.
If you still have pain I would work on your core strength ...
Try to sit on the bike on the trainer and pedal without touching the bar without sliding off the saddle. If you slide from the saddle-adjust the it. Your hands should be slightly resting on the bars/shifters to ride without neck pain.