'I have got', 'I have' are correct. 'I got' is incorrect.

"I got a pig" 没错，这句子只用法。你能说： 今天：I have a pig / I've got a pig! 昨天你买了一只猪: I got a pig!

it's very helpful to me. Thank you so much.

All of them can mean the same thing, yes. I have a pig is grammatically correct and is said everywhere. I've got a pig is also grammatically correct, but said mostly in Britain and not in America. I got a pig can mean the same thing as I have a pig in non-grammatical American slang, but is never said in Britain. Here in britain, it is grammatical, however to say I got a pig, meaning I bought/recieved a pig. Hope that makes sense :)