You've gotten terrific advice so far. In addition to mirroring her feelings, take some time in between thunderstorms to teach her how to pay attention to her breathing. For just a few minutes every day, work with her to count her breaths, 1, 2, 3, in…, 1, 2, 3, out. This is very centering and peaceful for most people (you may enjoy it, too). Help her until it becomes easy and habitual for her. Then begin to point out that she has some real control over her breath, and that can be a safe place for her to go to when something scares her that she can't make stop, like thunder.
Next time there's a storm, sit with her and do the breathing excercise, if she is able. She may not be able to do this for awhile, or ever, while she's freaked out. But some kids can use it, and it's a nice option to try.
But mirroring will probably be much more effective than reason at giving her space to sort through her own reactions. Let her have them until she doesn't any more. Let her hyperventilate, and even throw up, and don't act like there's anything wrong or unnatural about that. This will be hard for you, but try it; it may really start to turn things around.
There is also a fairly simple process used to turn around traumatic reactions called EMDR (Eye Movement Desensetization and Reprocessing) that has been very effective for a few people I've known. It is non-invasive and can be used safely with young children. Here's one link: http://www.webmd.com/mental-health/emdr-what-is-it