That sounds like some serious sleep deprivation, and the truth is that, especially when serious sleep deprivations is concerned, is that there really aren't a lot of easy answers.
You can try setting a solid sleep schedule (and keeping it no matter what, that means that even if you're not falling asleep you need to stay in bed, and at the set time for you to wake up, you need to get up, no matter how tired you are), exercising (but always more than five hours before you're going to go to bed), eating healthy, all that good stuff. I realize that you said no medicine, but the truth is that some simple OTC medications can actually help immensely. Melatonin is really quite good, it's a chemical that exists naturally in the body (and during the teenage years its production often dips, which is actually the reason why many teenagers have a hard time sleeping), anyways, you take it about thirty minutes before bed, and it just helps you drift off a lot easier. It helped me a lot when I was trying to re-establish a solid sleep schedule when I was getting clean and going through withdrawals. You don't want to use it forever, but, like I said, it helps a lot to establish the sleep schedule in the first place. It can be picked up for cheap in the vitamins and supplements section of pretty much any grocery store. For nights when you really need to get knocked out, you could try something with diphenhydramine (it is the only active ingredient of both Benadryl and Unisom). You want to be a lot more careful with it though, it's only for really difficult nights, it'll knock you right out... but if you over-use it you build up a tolerance pretty fast, and it can actually be addictive as well.
If none of that works, then you should probably go see a doctor because you might have a serious sleep disorder, and none of the advice you're going to get here will help.