This is a very common problem among people of all ages. Its a frustrating problem as well. Its very difficult to pinpoint the reason for anxiety. Often times anxiety is quite irrational which makes it difficult to control at times.
There are many things that can help with this.
Exercise is great for realiving stress that may show itself when your closing your eyes at night. Try getting a decent amount of exercise daily and sleep should come easier.
There are also some natural supplements that aid in sleep/Anxiety
Valerian root is very beneficial for helping with anxiety and insomnia. It acts as an alternative to benzosiazapines for releaving stress and tenision. It also has sedative properties. This can be purchased at your local drug store.
Melatonin can help regulate your sleep cycle. Its also been shown to have some stress releaving properties.
Kava kava is another one similar to Valerian in its function. It has a moderate sedative effect as well as relaxation.
Diphenhydramine more commonly known as benadryl is a great Otc sedative with very few side effects. 50mg should really help with sleep.
If the problem persists you should consult with a psychiatrist and get his opinion.
These would have been my suggestions as well.
Valerian, as quoted above is often prescribed in Europe for anxiety over a benzo.
It is more widely accepted in EU countries as a legitimate alternative.
I myself have tried it for anxiety and once I found the right brand had fairly good results with it.
When choosing an herbal supplement though it is good to go for organic and a reputable company.
The US has no regulations on herbal supplements so you can sometimes try one brand with no effect and another with much better results.
Yogi Teas is a good try for herbal night time teas. They have a box that is a variety pack specifically for sleep.
I myself found the Kava to work best but each person is different and you may find the others just as beneficial.
The problem I had with benadryl is that once you start taking it to get to bed, you need a sleep aid more and more.
Antihistamines are good sleep aids but trying something more natural, like an herbal supplement may be a better way to start.
I sometimes try doing some deep breathing when I'm having trouble sleeping, which is often :D
I do visualizations as well....imagining myself in peaceful natural settings, imagining my body going to sleep from toes to head etc..
Let us know what you try and what works for you!