Hi Melanie--
I've been there with you fairly recently, my dd is about 3 weeks younger than yours, but we went through something like this not too long ago -- a couple thoughts:
First off, if her sleep is that awful, you're in a miserable overtired cycle right now. She's probably screaming at bedtime because she's overtired. Someone (I think it was Laura) mentioned that when her ds was overtired like that, she'd drive them around mid-morning to let them catch an quick nap so they'd be ok for their midday nap -- which worked perfectly one day when dd1 woke at 5 AM ready to start the day -- she slept for about 20 minutes close to 11 and then was able to take her regular nap around 1:30 which meant she was doing better at bedtime -- this from a kid who would NEVER nap more than once a day since she went to one nap around a year.
From what I've read, early wakings are usually due to overtiredness and oh those after-midnight wakings are awful. Nothing that we do will get dd1 back to sleep if she wakes up anywhere after about 1 AM - seems like she just has to tire herself out and she'll go back to sleep (after about 2 hours
) -- I try to keep her in her crib unless she gets super upset. It's hard though, the way I look at it, if she wakes at 2 AM, she's been asleep for 6 hours, which would make her pretty rested.
If you think it's teeth I would give something for pain right when she wakes up and then sit with her while it kicks in. How verbal is she? Ours is super verbal so usually I'll lay on her floor and explain to her "it's nighttime, everyone is sleeping -- Mommy is sleeping and Daddy is sleeping and baby sister is sleeping...and I run through our whole family/friends...as well as all her stuffed animals. I'll sing her songs/tell her stories very quietly as long as it's not getting her more riled up. Basically, I think I'm keeping her in a somewhat sleepy state of mind and keeping her in her bed without her screaming all at the same time.
Basically, I've found that overtiredness is really the culprit -- try to keep her nap consistent and put her down a bit early for bed if you can. We've had to occassional early waking here (we've also got a new baby, so mass confusion everywhere), but we haven't had a middle of the night 2 hour party session for awhile (knock wood).
Hang in there, I know it's SO hard to have these middle of the night issues -- when they're up for hours and all you want to do is sleep.