Soldiers in combat try to fit 1 to 2 hours of cardio into their busy days. Weight training is more important for general health, but intense exercise is the best medicine for stress tolerance.
If that sounds impossible, then start with some realistic like 1/2 hour, walking, biking to work, moving boxes, and work up from there.
Overreaction to small upsets is a symptom of depression and it is one that SNRI or SSRI drugs such as Vanlafaxine and Sertraline are effective for. Generics are very cheap even if you don't have health insurance, and your primary care practitioner is trained to prescribe them.
The above measures are intended to build up your base so you will be resilient without trying. Spare time activities in the areas of pets (e.s.p. raising chickens), religion, volunteer activity are also helpful.
I was a long time practitioner of
a self-help approach aimed at training the mind while in action. Today I think that repeating mantras and phrases fills up my mind with more junk and makes managing harder. If I repeat a mantra I won't repeat it quickly but will try to repeat it at the moment a distraction comes in.