I understand what you're going through. Sleeping and resting are two different things. Sometimes you could sleep for 14 hours and wake up even more drained than you were before. And sometimes you sleep only 3 or so hours, and wake up totally refreshed.
This is purely psychological, and has nothing to do with being physically tired. You could exercise as much as you want, you could do the most physically demanding activities all day, in itself it's not going to force you to rest.
I, too, would drop sodas/energy drinks. They would only make things worse than they are already. Coffee, while is quite useless on people with this problem for some reason, is at least not as destructive as the aforementioned drinks.
And while I agree with
>>5110 about carbs and sweets, I certainly believe that diet has nothing to do with this.
I believe what would really help is to somehow try to be at peace with your mind, even if just momentarily so. I know it's difficult. And look who's talking, I pretty much fell into the same situation, though I can't even sleep more than 4 hours on a good day, let alone have any rest. But give it a try, if you could let your feelings go before bedtime, only if for a day or two per week, you could get some rest.