You can never say "it's hurts". This is incorrect English.
You can say "It's hurt".
For example: "How is your arm? It's hurt." That means something has happened in the past that hurt your arm. It means your arm isn't working properly now.
You can say "It hurts".
For example: "How is your arm? It hurts." That means your arm is hurting right now. You can still use it but there is pain.
"It's hurt" and "It hurts" are very similar and you can use both. Don't worry too much.