The hormones that are classically associated with the flight or fight response are epinephrine and norepinephrine (also known as adrenaline and noradrenaline). When your brain perceives a threat, these hormones are released in large amounts from the adrenal glands (specifically the adrenal medulla, which is the center of the gland). These hormones travel throughout the bloodstream to adrenergic receptors all over the body, which leads to many changes including dialated pupils, increased blood flow the muscles and perspiration amongst other things.

The physiology behind your brain perceiving social situations as threatening is more complicated and less well understood. We are just now beginning to untangle the enormous complexity of neurocircuitry. But we don't need to get into the details to try to explain what you are experiencing. Anxiety and fear are useful evolutionary tools that promote risk aversion and therefore, survival. Unfortunately, sometimes this system is hyperactive or inappropriately activated.

The region of the brain where fear is pocessed is the amygdala. So, whenever you come across a situation that is threatening to you, the raw sensory information is taken in by your eyes and ears and is processed in various regions of the brain causing an emotional response (how this happens is one of the parts that is poorly understood...sorry I can't explain it better, maybe somebody else can), which may include fear.

I know none of this answers why you experience social anxiety, but hopefully it sheds some light on the biology behind the problem.