I was like that when I was younger. I think my adrenals were going 24/7, but then whatever part of brain must've burned out because I now have the opposite problem (even been diagnosed w/dysautonomia).
Theoretically, clonidine could reduce some of that -- it acts on the brain/brainstem and reduces sympathetic outflow. I think it only reduces alpha-receptor outflow, though, so heart rate wouldn't be effected. It's normally used to reduce blood pressure, so that could be a problem if it's already low. I've taken it a few times, and as far as anxiety it feels to me like anti-caffeine.
http://en.wikipedia.org/wiki/Adrenergic_receptor