That instant-fear reaction to common stimuli is a symptom of PTSD, and is the reason that I flat-out refused pager duty after the first ~6 months. This system should be considered a workplace hazard; it has a measurable detrimental effect on employee health, and not all employees recover afterwards, as you and I are discovering for ourselves.

Systems like pager duty should be reserved for temporary crises, and should only notify people during their work hours. If a company can't afford three emergency-ops people, then they are probably overestimating the cost of downtime. If the company expects more than one incident per year, then they have a QA problem, not an ops problem.