What is a quick technique to get rid of anxiety instantly without medication?

No quick fix. Address or get out of difficult or chaotic situations. Go into challenges prepared. Ask, "What is the worst that can happen?" Set realistic goals. You cannot master all fear any more than you can master life. Do not avoid difficult tasks, but take them in manageable portions. To be brave, act brave.
See below. Are you anxious about every day stuff or particular events?Generally, it's good to know what makes you anxious. Practice relaxation, mediation, guided imagery (you can google it); keep a diary of the events when you happen to be anxious -- what happened (the event), thoughts you had; things you've done to decrease anxiety; how you body responded (where did it feel in your body).
Some people tout. Roger Callahan's "Five minute Phobia Cure." The technique, among many things, involves tapping various points on the body. Some claim this is miraculous. I haven't had this success, personally. The more protracted approach seems more prudent--come to understand your experience, using a mental health counselor, and then systematically undermine the symptoms with good mental health practices.
Biofeedback. SLEEP:Avoid drugs for sleep, weight loss, nervousness, anxiety and wait gain. Usually try behavior modification, punctuality in sleeping, read a book and warm milk fi u like. Avoid caffeine, drinking, TV in room. Do regular exercise. Once on drugs for sleep u mau find it hard to regain ur self control.Use drugs only if a MD dx of symptomatic insomnia.
Breathe !! If you can find a quiet place - do so. Breath in slowly & deeply through your nostrils. Fill your lungs with air (but not to the point of discomfort). Hold for a count of five then slowly begin to exhale through an open mouth. Repeat at least 12 times, longer if you need to. If you haven't been assessed for your panic/ anxiety - that would be prudent. Anxiety is no fun BUT it is treatable.