Every single doctor or nurse or dentist who's ever jabbed a needle into me has always said those exact same words beforehand. They must all learn from the same playbook.
I understand why "pinch" is their word of choice. It certainly sounds less dire than, "Brace yourself, I'm about to plunge this big needle through your skin and into your flesh." A "pinch" is something a girl might do to you if she doesn't know how to fight and inflict any real damage. A "pinch" of vodka is a trace amount that you theoretically won't even feel. (Of course, I've never heard anyone ask for a pinch of liquor who didn't really want a big dollop.)
But the fact is, "pinch" is not an accurate description of how a needle feels. A "small stabbing" would convey the actual feeling more accurately. I have to admit, though, that once my expectations have been managed so adroitly, I am more relaxed.
None of this is to suggest that all of these doctors and nurses are not perfectly pleasant. The nurse who administered my shingles vaccine yesterday even added, "This one doesn't even go into the muscle, it's just a sub-cute." Which I guess is the cute way of saying sub-cutaneous.
In fact, this particular nurse was not only pleasant, she was insightful as well: she evidently has the ability to recognize a coward when she sees one.