T.S.
Please talk to your doctor about your concerns, and/or take her to see a dermatologist.
I imagine they will tell you her skin is JUST FINE.
I am extremely fair and had a horrible, all over my body blistering sunburn when I was 11. I was literally in tears for two full days, it was awful.
I am diligent about sunscreen, for sure, both for myself and my kids. But do burns sometimes happen? Sure. Not often, but it happens, especially when your kids get older and start spending more time away from home (especially if they go to summer camp!)
I think you need to stop being "sad and mad" and accept that this was a one time, unfortunate mistake.
As much as we attempt to control every single thing that affects our children we just can't do it. This won't be the last time something like this happens. A few months ago I had to go pick up my intoxicated daughter from a party, now THAT was hard!!! She's a high school senior and prior to that had never gotten into ANY kind of trouble, so it was really upsetting. No mom should ever have to see their "little girl" that way, but like I said, these things happen :-(