Lindsay,It sounds to me like you are hyperventilating when you get really upset and anxious.
The body is a very sophisticated machine so there are obviously some extremely complicated things going on inside when a person hyperventilates. Basically, what happens when you hyperventilate is that you start breathing excessively fast. In other words, you begin to take in more oxygen than your body generally needs.
This hyperventilation or rapid breathing can be caused by any number of things but is often associated with stress and anxiety.
In the case of panic attacks, it is quite common for a person to hyperventilate as their stress level increases. Their breathing will become more and more rapid which can then lead to lightheadedness and other symptoms often seen with panic attacks. Source: EzineArticles
One of the best things to do when you are hyperventilating is to try and control your breathing and to slow it down.
If you are routinely dealing with panic attacks or still concerned about your symptoms do make an appointment with your physician.