I agree with Mark. If I move my neck around too far/quickly, I'm in trouble.
Has your neck been examined, thoroughly?
If you know you're going to be in a situation where your neck could get jostled, you might want to consider wearing a cervical collar for stabilization. (Don't know if that would be practical for a haircut, though.

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When I have headache, I find "collaring up," helps calm things down. I sustained an incomplete spinal cord injury and my neck is not stable.
My PT believes my quality of life would improve dramatically if my neck was stabilized with metal rods. My neurologist feels, given the damage to my spine, that any surgical poking in that area would be too risky.
So, for now, I keep my collar handy.