'I know, I am' indicates a different tone the way I see it. But maybe I'm wrong. What type of sentence is 'I know I am!' ?
- "I know, I am." or "I know—I am." is essentially two statements. They could be a response to a reminder ("Remember that you're supposed to take out the garbage. - I know, I am [taking out the garbage].").
- "I know I am." is probably one statement with subordination, equivalent to "I know that I am." It could be in response to a comment about the speaker ("You're the youngest person in the room! - Yes, I know I am.").