Thanks for relating this experience. Real demonic possession is rare, and it requires a trained and experienced exorcist to deal with it. Yelling at the person, stringing together Bible verses, "in the Name of Jesus..." and so on are just theatrics that deal ignorantly with the afflicted person's psychopathology.
Furthermore, the anguish of mental illness can be multiplied by such tactics. Exorcism is not for most people, even very holy folks, and should never be attempted on one's own.
Jesus called Satan "the father of lies." That alone should trip up anyone running with Bible in hand to evict a demon.
Finally, I was glad you were able to ascertain that the woman in question is well now.