You'll will get every conceivable recommendation, from "keep your hybrid" to buy an XYZ road bike with DI2. You need to supply basic information: age, experience, conditioning. general location (terrain), types of roads/trails (any unpaved?). You will still get the same range of recommendations, but with a bias toward the reasonable.
You're not going to get on a road bike and feel as comfortable as on your hybrid. The position, even on a relaxed geometry, will be different and increasing comfort will require a good fit, increasing your core strength and probably using your leg muscles are somewhat differently. Do you have any friends with a spare road bike you can try; this is a risk since you'll jury-rig the fit, but it may give you a feel. Or rent a road bike for a few days from a shop that will do a quick fit.
If you're riding on anything but paved surfaces you'll want a bike that will take at least 28mm tires depending on your weight. If it rains where you live you'll no doubt want to be able to install fenders .
Take your time, find a few LBS that are interested in more than a quick sale. Whatever the bike fit is everything.