Well I started having horrible panic attacks when I was 15 (4/5 years ago) and I noticed I would get them in small, crowded places (mostly buses and malls). So I understand, I would try to slow my heart down by not breathing, but IT MAKES YOU FEEL WORSE! (I have recently started noticed my panicy feeling coming back again (mostly when I don't take my medication, but I take xanax and I don't know what I would do without it. I did good without it though for some time and here are some tips if you can not go on medication.
My psychiatrist gave me a really good exercise (it's not a breathing technique because they don't work for me.)
You sit down with your feet propped up and start from one side of you body to the other side. You close your eyes and slightly open your mouth with you tongue touching the roof of you mouth. Then you put your arm up and tell your self that it is getting warm and expanding then do this with like your fingers, legs, feet, etc. (It's a slight hypnotic thing)
But since you can't do that in public, try just going to a restroom and closing your eyes for a few minutes, to get your breathing back to normal or think of the ocean and a hot breazy day or something relaxing.
(I have yet to find something that naturally cures me, mine kick on when I'm not even worried or thinking about anything.)