There are quite a few things that could be going on here because the trapezius is involved in both the neck and the shoulder functions. You could have injured the joint between the first rib and the spine because the first rib lies directly beneath the upper trapezius.

An alternate source of the pain and click is due to the deep surface of the scapula rubbing up against the ribs just at certain positions.

To fix ( and this is just a guess as we cant really examine you) It would be worth doing your strengthening in prone on the bench and working on very slowly letting the weight down ie eccentric strengthening of the rhomboids and doing lots of stretches to the upper trapezius and scalene muscles.

I would encourage you to sort this out properly as you may be doing long term damage to the Wikipedia reference-linkrotator cuff tendons if you are overtraining some muscles but undetraining others and giving yourself a muscle imbalance issue.