Saw your post, didn't want to read and run!
It could be teeth, but my DS I sometimes find (occasionally) that he wakes out of habit. For a few nights on the bounce, he'll wake at exactly the same time and have a shout. He also fairly regularly wakes up and chats to himself, then falls back to sleep. Chatting; ignore. They're fine. If your DC has been sleeping before this fine, I suspect it could be waking from habit and being unable to get back to sleep, which must be so frustrating for her.
If crying starts, I leave it 10 minutes before going into his room. I leave the lights off (landing light on), and go in with a low, calm tone. I pick him up and give a cuddle & cold water (how many times have you woken up thirsty, especially if the central heating is on now it's getting colder?) and resettle. I give him 5 minutes, timed on a clock and I just wait outside. If he still isn't calm, I go in again and offer calpol straightaway. Maybe that's a bit trigger happy, but no amount of cuddles and soothing is going to cure a headache. I'd hate to be denied pain relief for a nasty headache.
Also, do you have a sleeping bag for your DC? They can thrash up and down as they become more mobile and kick off their covers; but they can't get them back on.
If all else fails; it really depends on your style of parenting. You can either go in and resettle for as long as it takes every 5 minutes or so, or take her into your bed. Either way, you need to reinforce the idea that 3am is not the time to start the day.
Hope you get a solution soon x