I have bad neck spasms, could this be due to a plate to reset my clavicle?

Possibly... Best to let your doctor answer this question; this may be the cause, or your may suffer from degenerative cervical disc disease. A visit to your primary care physician is appropriate.
Yes. Certainly this is a strong possibility and the plate may need to be removed. There are other possibilities including your initial injury or other neuromuscular problem. Go back and speak to your surgeon.