I don't know but I was afraid also when I was young child.
For me it was the anxiety of going to the clinic to get a vaccine and not that actual vaccine that freaked me out when I was young.
Parris Island Marine Corps boot camp cured me of fear of needles. The visits for innoculations were almost a relief from normal harrasment/training. I went through at a time when physical abuse of recruits by drill instructors was the norm. You needed to be #1 or invisible--everyone