English question, please help.?

It is not grammatically correct.

A native speaker would say:
My hand hurts
My foot hurts
My back hurts

We would generally use 'pain' in a general/non-specific phrase such as 'I'm in so much pain.' Then someone would ask 'Where?' and we would answer with 'My hand hurts.'

You could also say My hand/My foot/My back *is in* pain.

My hand is in pain.
My foot is in pain.
My back is in pain.

I would say "My hand hurts."

But saying "My hand is pain" isn't necessarily incorrect... it'd be a metaphor I suppose.

Almost. Say: My hand is in pain. or: My hand hurts.

My hand hurts.

No, you'd say 'my hand hurts', 'my foot hurts' etc. You might say 'my hand is in pain' but it doesn't sound as natural.

No it isn't. Pain is a noun not a verb. You can say - 'My hand is paining.'