The answer is no. Panic attacks do not damage your heart. What occurs is that your fight or flight response is activated by a trigger, which in this case may be from your heart beating faster, palpitations, and chest pains. You might interpret this as you are having a heart attack, and it is this thought that makes you anxious. The anxiety then sets off your fight or flight response, and your sympathetic nervous system is activated, which increases your heart rate, and it also signals for the release of adrenaline into your bloodstream, which travels to the heart and also increases your heart rate- this culminates in a full-blown panic attack. The panic attacks only last for a few minutes, then the heart rate goes back down to normal. Alas, there is no lasting damage to your heart.