Hi Skater,
Your reaction to stress is perfectly normal and nothing to do with diabetes. When you are nervous or stressed the heart pumps faster, making the heart pound and blood pressure rise; some people experience palpitations. Muscle tension increases, leading to headaches, dizziness, jaw ache and even insomnia. The mouth goes dry, digestion slows causing "butterflies" in the stomach. Breathing is faster and less efficient which can lead to over-breathing (hyperventilation) and breathlessness. Changes in the flow of blood to the skin cause sweating, blushing or clammy hands and feet.
Unfortunately when you look at many of these symptoms you can see how similar they are to those experienced in a hypo.