Hi K. :)
It sounds like you might be dealing with something called Night Terrors. They are pretty common with toddlers - usually starting around age 2 or so, but what you are describing sounds exactly like this.
My daughter began having them when she was about 2.5. We had no idea what was going on - she would just wake up and scream for a few minutes, sometimes much longer. She was inconsolable, and would even thrash or run around her room until it passed. It was terribly upsetting for both myself and my husband, because we just didn't know what to do.
Night terrors are different than nightmares. In a nightmare, your child will wake up as a result of something scary, and feel panicked. During a night terror, your baby is in a deep sleep, and she will not likely remember anything about it after it is over. It's kind of like sleep walking in that way, so you don't want to do anything that will startle her (like shaking her out of it) because that could put her in shock.
They are usually a passing phase. Our daughter has gone through two phases like this, both during times of family transition and lengthy disruption from our normal routine. The best things you can do: keep things calm arond an hour before bedtime - read stories, give her a warm bath, turn off the TV, etc. If and when she has another, stay with her, try calmly saying her name and holding her, maybe even turn on the lights. For our daughter, we ask her questions (do you want to be held? would you like some water? etc., sometimes sing her songs, and gradually she slips out of it and goes right back to sleep.
HTH,
R.