Are these correct?
1. Welcome inside my house!
2. Welcome in my house!
Context: A girl in a Youtube video, welcoming the viewers inside into her house.
Note my changes to your layout above. The question including "these" should have come before the two sentences.
As the others have said, "to" produces the natural expression.
Welcome to my house.
Welcome to my home.
Welcome!
We use other words when we're describing what someone else is doing/did, rather than as direct speech.
Helen welcomed me into her house.
Helen welcomed me in.