In lang=en terms the difference between agonize and hurt
is that
agonize is to struggle; to wrestle; to strive desperately while
hurt is to undermine, impede, or damage.
As verbs the difference between agonize and hurt
is that
agonize is to writhe with agony; to suffer violent anguish while
hurt is to be painful.
As an adjective hurt is
wounded, physically injured.
As a noun hurt is
an emotional or psychological hurt (humiliation or bad experience).