I agree with you that "screaming" in your sentence functions adverbially.
I wouldn't call it an adverb.
I hope my response will be of some help to you.
Please pay more attention to your punctuation next time - a period/full stop, comma, etc.
And I quote from one of Rover_KE's posts: 'Thread titles should include all or part of the word/phrase being discussed.'
('The maid had run screaming' would have been a better title.)
Student or Learner