I am so sorry. I have a 9 year old boy who was like this for many years. In his case I always had the impression that the pain was physically felt (not dramatized for effect) but that it was linked to frustration/anxiety/embarassment.
I just googled this link to make sure I wasn't crazy. Here's an interesting article.
https://www.intelihealth.com/article/pain-anxiety-and-depression-a-challenging-trio-to-treat?hd=Minding
Is your DD otherwise a bit anxious? If so, I'd focus on anxiety management and suspect the overreaction to pain will subside as she gets anxiety under control. We have used some mediation techniques with my son but the biggest change seems to have occurred when we took gluten and food coloring out of his diet. The change in behavior was dramatic. Things that used to make him explode now roll off his back.
Although a bit inconveinent, I think diet experimentation is well worth the effort. In my experience, we saw a dramatic change within 3 days. But if you're going to try this, make sure you don't let any gluten or food coloring sneak in. Food coloring in particular has an immediate negative effect on my son's stress/anger management skills. Weird but true.