I also have anxiety issues that have been disabling all my life. I also don't like benzos because they drug/fog my head too much as well as too much sedation, plus a lot of other side effects that make me really dislike benzos.
For stress and anxiety I highly recommend: Meditation (Vipassana & Shamatha), Hatha Yoga & Asana, a good diet, healthy rejuvenating sleep, exercise, eliminating unnecessary aggravating factors (like misuse of stimulants, stressful companions, too much TV & movies, many things misused or not in moderation can contribute to stress and anxiety).
It's said that "virtuous" behavior in daily life (best when practiced with integrity and consistently for some time) is a fundamental contributor to peacefulness, relaxation and being anxiety-free. I've found this is profoundly true in my life. To define my meaning of "virtuous" I point to Buddha Dharma teachings.
I have a "friend" who is severely and chronically afflicted with anxiety and stress. He is the personification of mischievous to downright evil. His life is extreme and over the top, and it's obvious why he's burning out fast. (I'm not implying anything about your life, just sharing everything that is of consideration for stress and anxiety relief)
Loving Kindness meditation (Metta / Maitri) is said to be very powerful for eliminating or reducing anxiety. Again I've personally found this to be profoundly true.
When the body is in poor health or imbalanced chemically or nutritionally it can cause all sorts of horrible effects like anxiety, depression, etc.
When I eliminated TV & movies altogether I found it a powerful benefit in so many ways. My mind became so clear and peaceful. TV & movies are such a powerful drug, people take it for granted how dangerous they are. They produce tolerance and really miserable withdrawals like any chemical drug, along with so many other drug like effects.
The withdrawals and addiction to TV & movies were fairly challenging for me to overcome. But now I'm off of them it's extremely easy to stay clean. The benefits to being clean are so great I have no urge to sit in front of a video screen. Plus it's so boring and lifeless. Real life activities are so much better, for body, mind and happiness.
I put everything I've mentioned here into practice in my life and it really works, perfectly and miraculously. But I'm very consistent and have been applying it for a long time. It takes some time and consistent practice for the best effects to appear. The longer and more consistently everything is maintained the more effective it is, as well as how many of the practices mentioned are incorporated, and how skillfully applied.