"I came home" describes the action of coming home. "I got home" describes the completion of that action. Practically, they mean the same thing. However, in the example you gave of updating your fb status, the best way to say that is "I'm home."

Question: When I arrive home at 7:00 p.m. from work and I write it down on FB at 7:05. "I got home." or "I come back home"? Answer: In those circumstances, I would write, "I just got home." The word "got" indicates that arriving home was your goal, and that you managed to get there. The word "just" is appropriate because it means that you arrived home only a short while ago. I would use the phrase, "I came back home" when I wish to emphasize that I left my home, went somewhere else, and then returned to my home. For example, "I spent two weeks in Japan, and then I came back home." The words "came back" reinforce the idea that I arrived again at the place I started from.

Your missing a correct verb agreement. "got home" is past tense so it would be, "I just got home." "come back home" is a future tense and would most likely be used like to this, "I will come home."