When you look at how Emily lived her life she was obviously transgender. The grey man was trapped in a woman's body his whole life and resented Emily for it. The psychic is a symbol for gender reassignment and the electroshock therapy doctor is a symbol for transphobia and the damaging effects it has on a trans person. When you see Emily's dolls, you see that one has a penis. She also has pictures of gay men in her nightstand. When the grey man finally gets to say his peace, he says "I had to live in your body my entire life answering to your stupid name.'
When she blacks out and we finally see what happens in the mirror, she's getting possessed (you see her getting possessed in the second repetition of scenes when it gives you the closeups and extra seconds) and she's the gray man now. When the gray man looks in the mirror, he does not accept what he sees and bashes his own head into the mirror. We see his reflection shortly before it cuts to Emily's female form bleeding from the forehead in the reflection of the broken mirror.
The broken mirror represents her broken psyche and her shattered identity forced to restrain (or "keep at bay" the man inside. And when Emily says "I lived with a man inside me" Sylvia says "we need to find him". Emily responds with "I wouldn't know how to begin" which is because of the blind eye she's turned to the gray man her whole life. (In the movie, she refers to it as blacking out and "waking up doing horrible things".)