It sounds to me like night terrors. It's like the body is in too deep of a sleep and the brain is trying to wake itself up. There's not an actual dream occurring, and there's not much you can do about it. Resting your hand on her reassuringly can help and making soothing noises... but one way to help is to try to prevent them. Don't put her to bed over-tired. If you don't think that's the issue, then it usually happens about 2-4 hours after falling asleep. So what you need to do is before the time span of when it usually happens, go into her room and slightly rouse her. You don't need to fully wake her but gently rouse her a little at least to see if you can get her to change positions. That may be enough to prevent it from happening.
My eldest daughter used to get them frequently. They do outgrow them. They do NOT remember the night terrors... it's similar to sleep walking. The night terrors won't harm them. It's more scary for you than for her. Truly.
At this age, though, yes children can have nightmares. It doesn't have to be something "scary" but it can be about things that children find upsetting or unpleasant.