Rick Hanson in Chapter 38 ("Don't Be Alarmed") of his book Just One Thing discusses the human nervous system and how it has evolved to promote fear and panic. Sure, if you're an animal in the jungle, in danger of being eaten at any moment, that's an appropriate survival strategy. It's less apropos in modern life. In particular, Hanson notes:
In brief, separation and stability are illusions; the constants are unity and change. Clinging doesn't work.
The appropriate conclusion? Hanson says it's wisest be aware of alarms when they ring, evaluate them, and don't react inappropriately or disproportionately:
Accept that bad things sometimes happen, there are uncertainties, planes do occasionally crash, nice people get hit by drunk drivers. We just have to live with the fact that we can't dodge all the bullets. When you come to peace with this, you stop trying to control—out of alarm—the things you can't.
Keep helping your body feel less alarmed. I imagine my "inner iguana" lodged in the most ancient and fearful structures of the brainstem, and gently stroking its belly, soothing and settling it so it relaxes like a lizard on a warm rock. The same with my inner rat, or monkey, or caveman: continually softening and opening the body, breathing fully and letting go, sensing strength and resolve inside.