My impression is that your problem is not about "sexism", it is about that her wage is higher than yours.
Ignore it. Don't compare your success to others, compare it to what you want. It is the decision of your department, what is the value of someone's work for it:
- If her work is over-valued, it is their problem and not yours.
- If your work is undervalued, yes it is a problem, but it is independent from her wage.
It is very unlikely that you would earn lesser because you are a male. Typically, such organizations have a fixed or roughly fixed wage table.
Yes, she might have some "downwind", but you have probably no way to know, what is it exactly.
Check, how people typically earn with your skills and experience in the region and field. It can help to determine, what is the case about (2). And leave (1) to others.
P.s. I think, the most probable cause of this scenario is that the department needs your work, but they don't have budget for that. As the woman was employed, it wasn't so yet. Now it is already impossible to decrease her wage, and they can't increase yours. It is also quite possible that they overvalued the competence of the woman. Any department/company leader knows the danger of such scenarios very well, their name in my region is "wage tension". Typically they try to avoid them, but it can't always happen.
P.s.2. People tend to undervalue the worth of the knowledge on fields which is not so well known for them, and overvalue the worth of the ones where they are familiar. There is nothing bad in it, it is simply because if you know more about something, you also learned, how complex/hard is it. Check the woman, maybe she is not so bad, only different.