Sorry to hear of your anxiety problems Chernp. Anxiety can be a tough situation to rectify, I experienced it for a few years following a low dose LSD trip unleashing unresolved grief about my Dads death a decade ago. The anxiety from that manifested as OCD ideation (purely obsessional - say I saw a graphic image or movie for example, I'd get a repeating thought loop of the bad stuff which was pretty distressing, to say the least).
I went on meds for a couple of years, Mirtazipine to be precise. I found it helped anxiety related sleep problems and day to day anxiety in a good way. Side effects included increased appetite and weight gain (my metabolism is pretty good so didn't get too overweight, just a bit extra body fat on my skinny frame), extremely vivid dreams (which I do miss sometimes, man my dreams were detailed and weird) and tiredness in the morning for an hour or two. I found coming off it not too be too hard when the time was right also. I had Xanax as a backup when things got real bad but was very aware of the addictive potential so only used it sparingly.
Seeing as you want to avoid pharmaceuticals (and I don't blame you after a couple of years on them) , the best bet is to try out some of the suggestions offered already in this thread. What really helped for me was learning some form of mindfulness meditation. I got hold of a book called "Brain Lock" (can't remember the author off the top of my head) and it had some great mental techniques borrowed from old Eastern mindfulness meditation techniques. One of the techniques was being mindful of your thoughts and to notice when you start getting anxiety inducing thoughts, what you start to do is label those thoughts as anxious and observe it as an impartial spectator, like you would watching televison for example, and learn to not get emotionally attached to them thus eliminating the anxiety... Sounds simple but takes a good amount of willpower and discipline just like any skill in life that you need to develop. You need to be persistent to get results.
As well as labeling anxious thoughts, you can develop mindfulness by labeling damn near every thought that passes through that head of yours, from happy through to angry through to sad, etc. It can be a massive chore at first and a real drag but once it's assimilated through repetition and persistence you learn to gain distance from those pesky anxious thoughts but still enjoy the utter joy of living. I'm still learning and getting better at it myself but have got to a point were a bad thought can pop up but it usually doesn't cause the old pavlovian anxiety emotional response... Think of your mind as a large rock in a river and the thoughts as the water rushing by, you can't stop the stream but you can learn to be like the rock that is immovable and just let the water (thoughts) rush by unabated into oblivion, never to be seen again.
I still have anxious spots usually once a year or so but find that now, instead of it hanging around and clouding my mind and judgement for months or years on end it might only hang around for a week or so max. I thank mindfulness practice to this. I also throw myself into a project that requires 100% focus, that way there isn't as much room for wallowing anxious thought.
This may or may not work for you but the beauty is that you don't end up relying on anything but the power and strength of your mind to overcome the hurdles of anxiety that can pop up in life. Best of luck to you in your journey to find piece of mind, I hope you find it soon.
"The love I've made is the shape of my space"