I handle regular patrons fine—why do crises still wreck me?

You have already done the hard work. The daily flow of patrons no longer rattles you. That is real progress—do not dismiss it. But the crises are a different animal. They arrive without warning and demand everything at once. If you have no standing plan for them, each one lands like the first one ever did. That is not weakness. That is the absence of a method. Notice also: some of what "overwhelms" you may not be yours to carry. A library absorbs a person's whole crisis—housing, hunger, safety—and hands you the overflow. You did not create that problem. Decide what part is actually your job.