Hello there! I suffer from panick disorder as well, and although I am on medication, a lot of the healing process or prevention process is you and how you think.
I like to first establish why I am panicking, remind myself that panicking will not help my situation, and come up with a few rational solutions to the problem.
It could definitly take upwards of a month to train your body not to panick or just to be anxious and not panick. There are some great books out there that you may want to look into on how to deal with a panick attack.
I am 25, and had my first panick attacks at 18 - was able to recover without meds...Then they came back to haunt me at a low time in my life, around 22 years old, and I didn't have the mental stregth to ward them off, so now I am on medication.