I know the feeling you had - the night before my first OW dive, I couldn't sleep at all I was so worried. We went out to the lake and I was really, really nervous the first time. We went down and I was breathing like a madman, jerking around everytime I saw or felt something...it was nuts!
After awhile though...the equipment feels natural. You gain trust in it. You keep people close to you underwater for safety, or, you use equipment that is in and of itself redundant enough that you can dive solo and still be safe.
Start by diving shallow...it's psychological, but you know the surface is nearby and you know that if anything bad happens you can come up quick. You build on the confidence gained in the shallower dives, and you use that on more challenging dives.
I always wondered what would happen in an emergency...would I freak out, would I be able to handle it...about a month and half ago I had my 2nd stage free flow on me at 90ffw. Scared the hell out of me for a second...then, I just grabbed the reg, stuck it in my mouth and signalled to my friend that I was going up. He went up with me and I went up the whole way, bubbles flowing like mad. I even managed to make a safety stop with it flowing =)
That's why you keep you first dives easy - shallow, clear water, sunny and warm. Go easy on yourself, there is plenty of time to do freezing cold, deep, wreck or night dives. It's all the fun of this - learning as you go.
And good luck - you'll love it!