Hi Molly! I'm the same way! I don't do drops. In fact, people laugh because I scream in terror at the little plunge at the start of Pirates of the Caribbean. Thankfully, Walt Disney World has lots of attractions for those of us who aren't big thrill-seekers, and all but a few rides are drop-free.
In the Magic Kingdom, you'll want to avoid the flume ride Splash Mountain, which has a five-story plunge. You'll probably also want to avoid Space Mountain. This indoor coaster takes place in the dark and does have a few drops. The drops aren't huge, but the fact that you can't see them makes them feel worse than they are, in my opinion. You will love Big Thunder Mountain Railroad -- it has little dips but is mostly lots of speedy twists and turns.
In Epcot, there aren't technically any roller coasters. You'll love Test Track, which is a high speed car ride with a little dip, but not drops. When you're in line for Soarin' you'll see signs about drops, but there aren't any. The Maelstrom in Norway has a tiny backwards drop that you can handle. Mission Space has
simulated drops that may bother you.
In Hollywood Studios, you definitely want to avoid the Tower of Terror,
which is a series of drops. The Rock 'n' Roller Coaster has loops, but my family swears to me there aren't big drops. I haven't been brave enough to see if they're right. Some people have
problems with the simulated dips in Star Tours, but they don't bother me.
Finally, at Animal Kingdom, you'll want to avoid Expedition Everest and the
Primeval Whirl, both of which have some downhill plunges. I used to avoid Dinosaur because it seems to have a big drop at the end, but I've now figured out that it's simulated so it doesn't bother me. Kali River Rapids has some drops, one of which is fairly sizable, plus it gets you soaking wet, so I'll never ride it again.
Hope this helps!