Many people do overcome panic and anxiety without medications, or with temporary medications. Specific types of therapy from a qualified expert can be very effective. A consultation with your doctor would probably be the first step if these episodes are continuing, then a referral to a good therapist/psychologist if the doctor rules out any obvious physical causes.
I don't believe there is any short-term physical damage from panic and anxiety, as unpleasant as they are (I've looked.) Best wishes to you.