The basics for a sexual harrassment lawsuit are absolutely present if you can prove:
1. She is unqualified
2. She is indeed having a sexual relationship with the person who promoted her to the position
3. She was promoted over you specifically because of the sexual relationship.
4. (An added bonus) Her presence and constant badgering for information make you uncomfortable due to her sexual relationship with "the boss". "Uncomfortable" is a wonderful word in the world of sexual harrassment.
I say get a lawyer and sue for millions.