Why is my heart doing this and what is it called?

When someone is stressed or anxious there is a release of adrenaline like substances (Epinephrine, Norephinephrine) from the sympathetic nervous system. The sympathetic nervous system is referred to as the "fight or flight" system and it results in an increased heart rate, blood pressure, strength of contraction of the heart and even erflies in your stomach. This is a completely normal physiologic response to stress and is not harmful to the heart. Anxiety can cause chest pain like you are describing. Caffeine and nicotine can also worsen these symptoms, therefore you should avoid them. Taking slow deep breaths will help improve your anxiety. You could also try to think of a relaxing place or activity. Medications are rarely needed in extreme cases.