I think it should be "See how dirty I look!"
"see" is a verb. In this context it means "observe", "notice". It's an imperative.
It can also be taken as a question, the "do you" missing:
"See how dirty I look?"
This latter construction often has the sense of "What did I tell you?", "Didn't I tell you so?", "I warned you this would happen".
See what you've (gone and) done now?
See what a mess you've made?
But not necessarily:
See how it works?
See how I did that?
See what I mean?