Paper bag breathing. I would not recommend breathing into a bag, instead, proper use of breathing exercises (regular, rhythmic breathing while relaxing & counting numbers) can be effective. For details of how to perform those exercises, e-mail us we will send you details.
Hyperventilation. When having a panic attack the body goes into full-blown "fight or flight mode" with rapid breathing that blows off so much co2 that your blood chemistry is altered. By breathing into a paper bag (my favorite is one that recently had donuts in it) you rebreathe some co2 and restore you pH balance and thus feel physically better.
Maybe. Have you tried relaxation breathing? If you want to avoid medication for your panic attacks, I highly recommend the book: the relaxation response by benson. Read the entire book, then start doing the exercises as contained in the book. Start with 5 minutes twice a day working up to 10 minutes twice a day. Your panic should resolve. You will be able to stop an attack with the book's techniques.