Have you tried 5HTP? You should post this question under the substance abuse community (
http://www.medhelp.org/forums/Addiction-Substance-Abuse/show/77). Trust me, you'll get a lot of help and support over there. You are suffering from withdrawals and it's normal to experience insomnia. Did you go cold turkey? Or did you quit gradually?
Well, it's common to suffer from insomnia when you are quitting alcohol or any downer. Exercising is a good start, because that should keep you focused on being healthy, feeling good, and eventually tire yourself out enough to fall asleep. But... natural cures are hit and miss. Some people swear by Melatonin or 5-HTP. I'd suggest that you ask your doctor for hypnotic sleeping pill(Lunesta instead of Ambien since it's much healthier and harder to abuse.)
Your brain is telling you that you should be drinking, and the only way to get through is at least getting some sleep. Good luck on the wagon. Or off it... whichever.