Using the skills when a child is using the steps on you

My 11 year old has been saying things like “Please stop talking.” “if you keep talking I am going to plug my ears”. “I am not listening.” This happens whenever I am trying to do a correction. She will even say “How is it the kids are doing TSG better than you?” She does not want correction and talks right over me telling me to stop talking. Sometimes I don’t even get 1 word out. How can you correct when someone is constantly talking right over you? She will get louder and more insistent if I continue despite the interruptions. Thank you. She is our child that is incredibly sensitive despite her bravado and if you say the slightest thing that she takes offense to, then she becomes cutting and mean and will refuse to participate or do anything and will tell you to go ahead and give her MM or whatever. I do emphasize that she “chooses”. She is just like me in this area, which is a hard pill to swallow. Neither she nor I accept criticism or correction well. We are different in our responses somewhat, but bottom line is neither of us handle it well. Thank you for your help in this!