When I got my road bike, I had some of the same issues - afraid to take my hands off the handlebars, twitchy-ness, etc., and it was all because I wasn't comfortable yet. I have a standard "male" bike instead of a WSD. I have a really short torso, but I also have long legs and long arms, and it fit me better. Sometimes I felt too stretched out, but like I said, the major issue was comfort. I wasn't ready for how responsive, light, and fast my road bike was going to be. This may sound silly, but something that helped me a lot was riding my bike on a trainer regularly. It really helped me become comfortable with the position I was in, without the "environmental" worries. It helped me learn a lot of where I should be distributing my weight and how I should feel on my bike.
On the other hand, if the bike doesn't fit you right, you're really not going to be able to be comfortable on it. But, if you were fitted professionally, I would give it a little time before you sold it and bought a new one because you may just run into the same problems all over again.
Good luck!
"It's a little like wrestling a gorilla. You don't quit when you're tired, you quit when the gorilla is tired."
-Robert Strauss