meaning of ちゃってる / chatteiru


As far as I know, the sentence "入っちゃってる自分の世界" translates to something like
"I'm deep in my own world" or maybe "I went deep into my own world".

What I don't completely understand is "ちゃってる". Is ちゃって like "te shimau" /
"chatta" signalling an unintentional/accidental action here? But why "te" and
not "ta"? And why "te iru"?

