I'm not very experienced, but I have experience with being new to the road bike (I used to have a hybrid).

I suppose from your message that you have not been correctly fitted on the bike. I suggest that you find a bike shop in your area with a staff member who knows how you should be seated: height of the seat, position of the seat, position and length of the stem, tilt of the handlebar, etc. If you don't feel right, it may be because you're not used to the road bike, but it may also be because it is NOT right. You should expect to pay for this service (50$?) and also you might have to change your stem (can be inexpensive depending on a couple of variables, anywhere from 20$ and up).

Also, sending in the bike for maintenance (unless you're well versed in doing this yourself) would be a good idea. Among other things, maybe the brakes have to be adjusted, and adjustments vary according to bike types. I have learned that the Shimano handbook says to adjust my brakes so that they are about 2 mm from the wheel, so now that they are correctly fitted I just have to lightly tough them to get some braking effect, not push them all the way down (which I would have trouble doing when riding on the hoods). Also, you should eventually feel more stable in the drops than on the hoods... (You can read the "What's in the drops?" thread too.)

I hope this helps a bit! Riding a road bike is maybe not for all and everyone, but I'm quite sure it can be fitted for most. Of course you'll also have to learn a new way to ride and use your body, you may even discover new muscles, but it's not that hard. Don't give up on the bike just now!

Good luck! Keep us posted about how this goes...