Is it permissible for me to expose a girl on thent on the Internet after she refused to associate with me, and is revenge the solution to my psychological problem after being exposed to difficult situations that led to my depression?

You should praise Allah for diverting you from marrying a girl who engages in forbidden relationships and from living with a friend, as both could be better for you. Allah destines good for His servant, the wisdom of which is not realized until later. It is not permissible to seek revenge on the friend or to expose the girl. For whoever conceals a Muslim, Allah will conceal him on the Day of Judgment, and exposing a Muslim is a characteristic of hypocrites. Rather, one must repent, focus on their own shortcomings, strive to marry a woman of religion and good character, and accept Allah’s decree.