hurt [transitive, intransitive] hurt (somebody/something/yourself) to cause physical pain to somebody/yourself; to injure somebody/yourself
He hurt his back playing squash.
Did you hurt yourself?
Stop it. You're hurting me.
My back is really hurting me today.
Strong light hurts my eyes.
My shoes hurt—they're too tight.
hurt [intransitive] to feel painful
My feet hurt.
Ouch! That hurt!
It hurts when I bend my knee.
hurt (adj) injured physically
None of the passengers were badly hurt.
so, when we say "I hurt my back" we may mean "I caused it" (maybe, I bumped my back on the edge of the table)
when we say "my back hurts" we don't know if I caused it or it is just my illness that caused my back hurt from the inside.
what about "I hurt on my back" or "I am hurt on my back"?
What are the differences between "I hurt my back", "my back hurts", "my back hurts me", "I hurt on my back", "I am hurt on my back"?