Hi Intro, I have sleeping issues too, and I've had them ever since I was little. I have sort of mild anxiety, because I started to randomly have panic attacks for unknown reasons about a month and a half ago. My anxiety is worse at night, because for some reason, that's when I'm most likely to have panic attacks. I don't just have trouble going to sleep, I'm afraid to fall asleep, because I'm terrified of dying in my sleep and never waking up again. There's nothing wrong with my body though, because no matter how terrified I am of not waking up, I still do wake up every morning.
I must admit that I've never used alcohol as a way to go to sleep, but when I was little, I took Melatonin pills. Have you ever heard of melatonin or tried it before? It's a bit different from meds, because it's a more natural remedy. It's a natural hormone that the body produces, and it helps with circadian rhythm and sleeping. When it's dark, the body produces more of it to help you go to sleep. When it's light, the production of melatonin drops. However, sometimes a person's melatonin levels can get screwed up somehow by any number of factors (your sleeping pattern sounds rather inconsistent, which could definitely mess with your melatonin levels) Taking melatonin pills can definitely help with bringing your levels back to normal. You can also buy it over the counter at most pharmacies.
You're definitely right about exercise too, or just doing enough things during the day to tire your body out.