I'm not sure whether this is going to help or not, but in my opinion I wouldn't introduce a character like this, because:
1) This is a very static way of introducing her. Leave out the sexual aspect and she's not actually doing very much. It runs the risk of being an infodump about her mind, which is effectively saying "Here's what happened to this person before the story started" where I'd rather see what actually happened in the story. I would rather see her interacting with people and doing stuff that shows what she does through her point of view, what she's like most of the time and hints at what her problems are.
2) It gives the impression that this is what she does - in other words, that being troubled, guilty and messed-up is the main focus of her existence. That may well be the core of her personality, but that's different. Can she function on a day-to-day basis, hold down a job, take responsibility? The first time you see a character from their own point of view, unless there's a good reason otherwise, it's natural to assume that they're doing their thing. In the circumstances, this does seem to suggest that her normal afternoon is to break down in tears whilst w***king in the shower.
3) It's actually quite a complicated mental situation that you're looking to portray. "Simmering fury", "unnecessary risk-taking", "depression intercut with the need for distraction" and a number of other things would be easier to portray than her rather complex and self-hating attitude to having one off the wrist. Again that risks it becoming wordy.
4) Someone out there will accuse you of defining women by sexuality or some similar stuff. That's probably not true, but the question will be raised as to why she is immediately linked to sex and not the male characters. Whether there's a good reason or not probably isn't the point.
Sorry not to sound more positive, but it does sound like you're making it hard for yourself, so to speak. I'd be tempted to push such a scene further back in the book, once the character is established.