I know "I'm good "means I feel good /I'm fine which is the answer of question "How are you/How do you feel". Am I right?
- refers to the well-being of the person - like you said: I feel good, I'm fine;
- gives information about how are you;
- it can have specific meaning: I do not need anything, everything is fine.
Example by @anuk (thanks):
Do you need some water? No, I am good, thanks.
"I'm a good man"
- means that you do good deeds, you are kind, polite, charitable...
- gives information about what you do;
There is a very specific / special context, where "I'm good" gets (but does not have in itself) the meaning of "I'm a good man":
Are you a good man or a bad man? I am good.
He "I am good" means "I am a good man" only because of the speech trick, of not repeating some of the words in the question.