I'm going to give my coworker the cold shoulder
Why are you giving them the cold shoulder?
I hate her. My coworker made a stupid mistake and it caused a lot of problems to me
I get your point, but it's not nice to just ignore someone. You are expected to get along with coworkers.
It's retaliation, she can hate me.
But others at work will see this and think she is the victim. You may also have to work with her and if you refuse to then there could be disciplinary actions for that.