have you considered that she might be experiencing night terrors...I don't know because you didn't give much info on her state when she wakes up except that she is screaming (one sign).
I suffered from these as a child and still do to a small extent, which my husband just loves :). He hardly bats an eye when i wake up screaming now.
whatever the reason, it sounds like she's waking up scared...so i guess the first step would be to make sure that her environment is as secure (in her mind) as it can be so that when she wakes up in the middle of the night, she won't easily convince herself that she is in danger.
You've probably already done all this but since you didn't give much info i would say to make sure she has a night light and give her some good rules to use to help her feel safe....My little guy has a big picture of Jesus on his wall and we talk every night about how 'Jesus keeps the ouws away'...that works for him (and us since we'ver christian) but i would imagine a parent could try it with any strong figure that a child looks up to.
If it is night terrors you could talk to your peds. doctor to see what they suggest on handling it.
anyway, good luck! hope something works for you guys...