Wanting to switch from a hybrid bike to a road bike, just have a question?

My main reason is speed, on flat road i will usually keep between a 15-18mph pace, and I'm spinning as fast as possible already. I commute to work, and ride around town for fun. I know the riding position will change, but my main concern would be if it would be worth it to spend 600-700 dollars on an entry level road bike, just to get from point a to point b quicker. I know the tires will be quite thinner but will that really help me increase my speed? Or should I get like a fitness bike, with the thin road bike tires but with straight handlebars?