Why don't your parents want your doctor to prescribe medication for you? Are they anti-meds, or do they not believe there's anything wrong with you?

If you can't try meds (for now--when you're 18, you can make your own decisions, and the doctor can't give info to your parents without your consent), then how about trying changes in your diet and using non-medication techniques to deal with panic attacks? There are several good books with ways to get through panic attacks, and some foods are more likely to raise anxiety. I don't have any resources on diet, but you should find info by Googling "diet" and "panic attacks."

Check out The Anxiety/Panic Internet Resource.