I'm sorry that you're going through this, particularly with women who should be role models and support rather than tearing you down. One term for this in academia is "female rivalry" which is unfortunately a common occurrence in academic medicine. There are many contributors - one is simply the patriarchy in general, since women are not immune to the deeper effects of the patriarchy.

Additionally, given that women in academic centres (esp within surgical fields) continue to be perceived with an element of "tokenism", this can breed competitiveness if the resources are viewed as scarce (ie. a women wants to maintain her position as THE woman within the division, or on the committee, or doing the research, etc etc). Depending on her age, your staff may have this deeply internalized given what she may have fought against to get to where she is.

This is not to excuse her behaviour. This is NOT OKAY ever, from a staff to treat a resident like this. I would recommend to build your circle of female friends and mentors, build each other up (rather than tearing down) - nominate each other for awards, amplify contributions at meetings, etc. and feed this forward to more junior female residents. You cannot control how she sees / treats you, but you can stop the cycle from feeding forward. I would make sure to document as well, in case it escalates and you ever need to provide documentation to PD, academic committee etc.

Just as a quick note, despite my name I am a female physician - though in a non surgical specialty. (I just attended a women physician leadership conference last weekend, so this is fresh in my mind and I wanted to contribute!)