Hi!
I started with a Giant Hybrid, too! Welcome to the dark side! 
I just wanted to pop in and say give it time. A road bike definitely handles differently than a hybrid or a mtn bike. It feels different checking behind you for a car, no doubt. But with practice and time, it will be like second nature!
And regarding the bad spill...give that time, too. I lost it at the bottom of a hill a couple years ago, and I'm still scared when I descend. So I go slower. No biggie.
I hope you come to enjoy road riding as much as I have (and so many others here have as well). It's my favorite thing to do...I bet you'll find the love soon!
2007 Trek 5000
2009 Jamis Coda
1972 Schwinn Suburban
"I rejoice every time I see a woman ride by on a bike. It gives her a feeling of self-reliance and independence the moment she takes her seat; and away she goes, the picture of untrammelled womanhood."
Susan B. Anthony, 1896