With anxiety disorders, it is not unusual at all for one's heart rate to be rapid at times, and for one to be aware of their heart pounding, as well as other symptoms in that area of the chest, such as the tightness and uncomfortable feeling that you are experiencing.
This is actually a normal response of our "fight or flight" system. What is abnormal is when this response, caused by the release of adrenaline, occurs when no threatening situation is upon us. And anxiety symptoms can even occur when we really don't feel panicky.
The heart is one of the most powerful muscles in the human body, and these episodes, caused by panic disorders/anxiety disorders, do not typically cause any damage to the heart.
A good rule of thumb is to always have a complete physical examine to rule-out any underlying physical condition that might be causing these symptoms. If nothing is found, they are most likely caused by an anxiety disorder. At this point, treating the anxiety will provide relief from this heart related symptoms.
The very best to you, Alesha!... Chuck