Hi BWR and welcome to the A/P!
I am sorry to hear of your sleep problems...it is miserable, I know.
You are wise to seek alternative ways of getting to sleep. Medications are wonderful tools for helping us to manage our anxiety issues...but it is good to have other options for our use as well.:)
Here are some of the exercises that M.M. mentioned above...from our Resources:
Self Help sites with breathing/relaxation exercises instructions
Panic attack relief exercises:
http://www.healthcentral.com/anxiety/c/73076/34334/breathing-lessons/
http://www.healthyplace.com/
http://www.stress-relief-exercises.com/
http://www.ehow.com/video_4405003_breathing-exercises-panic-attacks.html
http://www.psybersquare.com/anxiety/panic_relax_I
Give them a try and see how they work out for you.
I also second Merrida's advice about exercise...as well as turning off back-lit devices at least an hour before bedtime. This includes t.v., computer and smart phones/tablets.
Sound wave therapy, or binaural beats can be found on youtube or as an app, and promotes theta wave (sleep state) activity that some find invaluable for sleep.
Best wishes and post with us anytime!
Scaredy Cat