What should I do about exposing my friend on social media in a moment of anger, and will I be held accountable for that on the Day of Judgment even if I apologize and she does not accept my apology?

As long as you are repentant, you must seek your friend's forgiveness for exposing her. If she forgives you, then there is nothing against you. If she does not forgive you, or if you cannot reach her, then you must seek Allah's forgiveness, increase in good deeds, and supplicate.