I’m home is the same as saying I am in my house.
Saying I’m home is much more natural and definitely what a native speaker would say. You could also say I’m at home.
-Where are you?
-I’m at home.
You can also use I’m home to announce your arrival into the house.
*opens the door*
-Hi, Honey, I’m home!
–Hey! How was work?
–It was a long day, I’m just glad to be home!
