Oh man, I understand exactly what you're going through. I've had the same problem my whole life (I'm 30 now). I still haven't found a total solution. Anxiety issues are extremely difficult to treat / help / fix. If you've got a brain that tends towards anxiety, no amount of good suggestions or willpower will ever really "fix" it.
However, that doesn't mean there's nothing you can do. As someone who has basically the same problem, I've tried just about everything people have suggested here and then some. One therapist foolishly tried to hypnotize me once, not realizing that my type of brain isn't hypnotizeable. I was even given sleeping pills several times, but none of them worked for more than a day or two. I built up a tolerance to them almost instantly. In a way, you can think of yourself as being exceptionally strong - immune to all that modern medicine can do to try to change you.
But of course, in this case it would be nice to be a little less strong.
All that being said, there are some things that I have found DO help at least part of the time. Some of them have been mentioned already.
-Making exercise - and I mean a LOT of exercise - a routine. Taking a walk before bed isn't likely to help in your situation, but if you manage to keep your body consistently exhausted, it will override your anxiety and force you to sleep much more easily. I'm talking about long runs or long periods of lifting weights or something. Hard to do regularly, especially if you're always tired and anxious, but very effective if you can manage it. Exercise is a very effective treatment for anxiety in general, although difficult because anxiety can make it hard to exercise.
-Avoid lit screens for an hour or two before bed. I didn't expect this one to work, but it does help. Electronics like phones and computer screens are designed to mimic the sun, and they send a strong "stay awake" signal to your brain that only makes sleeping more difficult. You can use a program like f.lux to take the harshest light out of your computer screen in the evening if you're not able to turn the computer off that long before bed, which helps a bit too.
-Don't use your bed for anything but sleep. This one is really important. Our brains associate locations with activities. If you do anything in your bed other than trying to sleep, start doing it somewhere else.
-Make yourself a bedtime routine, like a 3-year-old. You'd be surprised how well it can work - again, our brains can be trained like Pavlov's dogs - and you can have fun with it. Make up a chant or a rhyme to repeat before bed. Stand on your head. Whatever you want. As long as you do it consistently, it will eventually help, despite the anxiety.
-Tea. Not caffeinated - I find I have to avoid caffeine after 4 pm or I'll never sleep. In fact, it's best to avoid caffeine as much as possible if you have anxiety issues. The herbal teas I find help me are chamomile, melissa (lemon balm, though there's a type without the harsh lemon flavor), and mint. Actually, any kind of mint can help. Scented oils, anything. They have a mild sedative effect on the brain. I cycle through these teas so I don't get too much of a tolerance to any one. Might be a good replacement for the milk at least some of the time.
-This one is dependent on where you live, but in my area it's not illegal: as a last resort, I smoke cannabis before bed. It's not ideal because it makes it harder to wake up in the morning, but I use it in situations where it's really important for me to get to sleep. Not good to use it too often though, or it stops working, and you can also start to have different anxiety issues as a result of being used to being sedated all the time, as I'm sure you know if you have experience with any kind of tranquilizers or anti-anxiety medications.
That's all I can think of off the top of my head but I'll post again if I think of something else. I really hope this helps at least a little. Being terrified of something you know isn't rational, having anxiety you can't control, is a hard thing for people to understand if they haven't experienced it, but at least you've got one person here who knows exactly how it feels. Be strong - you'll find your best solutions and get back in control if you don't give up.