There is a big difference! I am fine indicates that you are in good health, feeling well. Unfortunately, it has become common practice for people to say 'I am good', when they mean, I am fine. It is colloquial and very common, particularly in American English, but in my view, not good English.

Actually, "I'm good" has several meanings. One is "I've had enough": Q - "Would you like some more tea", A - "No thanks, I'm good" Another is if you want to show off your skill at something: "I'm good at horseshoes" Yet another is to answer the question "Are you good or evil?" "I'm good"

There is not much of a difference they pretty much have the same meaning that you're doing well. In my opinion I'm good sounds better than fine. So you could say either one