Have got is non-standard English that is very common in spoken English, but should always be avoided in writing.
I have a car. (I own a car)
I got a car. ( I received a car)
Yesterday I got a headache from all the loud music. Today I still have that headache. (Not have got)
The exception is when the word got is used to express necessity. I have got to visit my mother before the weekend. (Again, this is more acceptable in spoken, rather than written English)