OK so, stubble + chin on cue = discomfort. I've experienced it, and soon learned not to shave too close. The stubble is just the start of what I'm assuming is your problem. Just thank your lucky stars you aren't using an ash shift, the grain snags like a beach.
I'm guessing the stubble is causing you a bit of discomfort, which in turn causes you to flinch ever so slightly. Because of this you kind of force the cue up into the chin as your head tries to move away from it to avoid the discomfort and you end up sort of straining the neck muscles. All movements are very minute but can make the world of difference.
Some players use varying amounts of chin pressure on the cue, and it can change over time as we get lazier we tend to rest the chin on the cue instead of using the chin as a guide. A former world class snooker player called Dott used to put a lot of pressure onto the cue, so much so he would player with a plaster (band aid) on his chin.
I could be way of base with you prediction, it could be something to do with a change in your cue action. If your elbow doesn't drop then as you reach the end of the follow through the cue raises up, and if you try to fight against it with added chin pressure this can also cause neck strain.
My advice? Don't play through any neck pain. Pack up and rest until you feel better. It simply isn't worth hurting yourself.