I have no idea, so I googled it... found some interesting answers. Apparently, by studying brain waves of infants and toddlers, scientists did find that babies do in fact dream and this peaks somewhere between 3 and 5 months. There is no way of determining what the babies were dreaming about, but it's likely their brains were working through their real life experiences (ie feelings of hunger, discomfort due to surgery, teething pain). I doubt that you have frightened your LO, though! It's possible she's teething and the pain from that is what's waking her as opposed to a nightmare... but really, how would we ever know. As long as you're there to comfort her when she wakes, that's all you can do! My DD2 just turned 3 and has occasional nightmares about monsters... you'll be comforting your little girl for many years to come!
