Are you new to this game? If so, then I think your body just needs time to adjust to the position. My arms and neck killed me the first few times I went out, but I just needed more time to strengthen those muscles and work on my flexibility. I've been riding less than 2 years, but it wasn't until recently that I feel comfortable in any biking position.
So don't push yourself to get into the drops. Ride on the tops and occasionally go into the hoods until it becomes more comfortable to ride in the hoods (it will eventually, but it will take time). Until you've developed more flexibility and core strength, the drops are going to be awkward and place strain on your neck and hands. All you have to do is keep riding, but build up your miles slowly.
If you are an experienced cyclist, then forget everything I said because I have no idea what else could be wrong.