You are experiencing anxiety. Your body is having an overreaction to a normal situation - your limbic system is freaking out and you're having the primal fight or flight response to a non-dangerous situation. Anxiety is uncomfortable but it will always pass. Check out this link for a great anxiety-reducing breathing exercise:
Cardiac Coherence / Biofeedback Tool: Inhale (5 sec) - Exhale (5 sec) MP3+Video - YouTube