What everybody else said! Poor fit could definitely cause this.
Also, just from my own experience, is it possible that you're uneasy about the drop bars mainly because you are so used to the flat bars? You're outside your current comfort zone? Every time I've ever gotten a new road bike, the first few rides seem a bit scary (especially my first "real" road bike), because it feels different than I'm used to. You have to adjust to the new feel. Sometimes, when I've been road biking a lot and not mountain biking much, I feel awkward (like I'm over-steering) on my MTB. The grips just feel wide, in comparison. I was thinking about getting narrower bars at one point, until somebody pointed out this would just make me over-steer more, if I really was. Then the next season I upped the mountain biking, and the issue went away.
I was just talking to my DH about this, because he got a new road bike yesterday (due to crashing his old one into the garage when it was on the roof rack on the car). He kept saying how twitchy the new bike feels, and he was afraid to stand on hills. I suggested he just take it easy until he gets used to the new geometry, and not even try doing anything that feels iffy, even if he normally does those things with no problem. He's nearing the end of 6 months of chemo, so he's not in his finest physical condition, which doesn't help.
The Warrior Princess: 2008 Jamis Xenith Pro / Bontrager Affinity 1 (men's)
2006 Trek Fuel EX 9 / Bontrager Race Luxe
2007 Trek 520 / Serfas Terazzo
Amelia Pond (She travels long distances, has great adventures, and she's a redhead): 2007 Trek Pilot 5.0 / Bontrager Affinity 2 (men's)