We friends went to zoo in cars. I came with my friend and now my other friend was insisting me to go with him,
I said, I came with him , If I go with you he will mind.
I have a problem with the form of verb. Is goappropriate or should it be went?>
If indicates a hypothesis, not anything certain. It is irrelevant to the meaning whether there is really a chance or not.
If I go is either about the present or about the future, but it indicates a logical connection, not possibility or probability. By "insisting me to go", I think you mean "insisting (that) I go", which would be about future going (something your second friend wanted, not necessarily a real future). I think "If I go" fits your context.
If I went is either about the past or about a hypothetical time, not a real time, that may even be contradicted by reality.