Can you get bloods taken for something so she can see you being all calm and might help her be less scared about getting them done? Mine have had a couple of tests, but have always seen me getting some taken for various issues (pregnancy, thyroid, iron etc) so mine never freaked out.

Having said that - my sister still freaks out and she is over 40! I remember a few years ago taking her for a blood test and I had to hold her down - luckily I'm much bigger than her LOL