What you are describing is known as palpitations, and they are quite common in people with anxiety. Palps can be simply being aware of your heartbeat, feeling it beating in your chest (as you are), or palps can also be missed or skipped beats.
I would say that it is probably one of the more common symptoms of anxiety. I know it is really scary. But, palpitations are generally no cause for alarm. If you can distract yourself, and not worry about them, you will find that you will experience this less frequently.
Good luck to you, Emski.