I don't know anything about insomnia, other than nothing probably works. But it's best to cross everything off the checklist, though. If it'll save you from taking meds. Never fear, Dr. Renly is now on board the HMS BGSF!
What are your eating habits? Do you eat fruits and vegetables? Maybe you are lacking nutrients. Do you consume caffeine? Maybe you need to lay off it. I was gonna suggest exercise, but it seems that's not working. Uh oh.
Do you have a partner? I know males tend to get sleepy after performing the ceremony of life induction. Not trying to be creepy, just being doctor like. Nothing's off limits or weird for a medical doctor!
It probably wouldn't work, but maybe you need to reset your sleeping schedule? I know sometimes when I drop the ball, it's what I have to do. Keep staying up until a decent hour like 9 or 10, even if it involves an all nighter or two.
Are you thinking too much? Pondering the meaning of life prevents you from falling asleep.
What's the temperature of your room? Warm? Cool? I can't sleep if it's humid, but if it's a bit cool, I get curled up in my blankies and get all cozy like.
Have you ever heard of those Bob Marley anti energy drink things? I tried one before going to religion class, and the combo knocked me right out in class. I would not advise it if you have any possible medical issues, but since it's an everyday item found at a convenience store, it's no different than suggesting a soda pop. But treat it just like an energy drink-drink responsibly. But then again, you said you don't want to go on meds, and I'd consider that a chem, I'm just simply trying to get everything out onto the field here. We can't leave any stone or option unturned, but because an option is available, doesn't mean it has to be taken.
If your suffering continues, see a real doctor, please. The last thing we need is for the British Empire to be closer to extinction.