Yes it is actually very common for anxiety to cause the heart to hurt! Like cj29 says, we are not easily convinced that worrying can cause a physical problem like pain in our heart for example. I have experineced the same thing, and thought it was a physical disease, until I learned it was my own worrying, anxiety. Hope you're feeling better.
I am sorry that you are dealing with this right now. In my experience with anxiety, especially when we worry about our health, I tended to focus on what I thought might be a problem. My concerns were with heart health, so naturally I would focus on every little palpatation, twinge, pain, etc in my chest; and it drove me up a wall. Your doctor says that you are okay, which is a great thing by the way, but that sometimes does not reassure us when we think something is wrong. Plus, you are really young, which is also a good thing:). Now, do you have access to counseling? For me, just talking about my worries and understanding why I was thinking the way I did, helped me overcome this...keep us posted!