There is a condition called Vasovagal syncope, which can result in fainting from injections. I should know, I've had it all my life and my daughter has it too. It's not a "fear" thing, it's a physical reaction and I'm told by nurses it's far more common than I believed. Earlier in life I was ashamed of this thing, now I confidently just go up to injections, tell the nurse I'm prone to it, and voila they always have a bed to lie down on during a shot (which for some reason often prevents it).
If this is as common as the nurses tell me, and people avoid their vaccines because of it, they truly are pussies.