Was in quite a similar situation as you. Initially thought it was a stiff neck but found out it was something worst when I went for a massage.

The pain was not so much on the neck but more toward my shoulders and back. Most likely a torn posterior deltoid. Took me two whole months of layoff to recover (due to my advance age). To date still have not returned to the gym.....  The thought of starting all over and the painful doms during the 1st weeks, maybe next month.

I suspect going too heavy  with the reverse flys on the pec deck machine which was the 2nd last exercise I did.

Last was shoulder superset - 20 reps front rise + lateral rise + bent over rise + shoulder press w very light weight.

The pain only came the next morning that was why I though it was a sprain neck.