Hi there. There have already been a lot of good comments in response to your question and fit is clearly important. However, what you've said and OakLeaf's points made me wonder whether where you are holding on to the handlebar may also be an issue. This is because I felt much like you described the first time I rode a drop bar bike. It had old style brakes without the rubber hoods over them that you now get. Because I wasn't confident about riding bent over on the drops, I held on to the top which felt narrow and difficult to steer with.

When I decided I wanted a touring bike with drop bars many years later, being able to hold on to the top of the hoods was a real revelation to me. The transition from a straight bar didn't seem so daunting then. This may be irrelevant in your situation but I thought I'd share that experience just in case.