Should I quit my job?

If her complaints aren't valid start looking for new work. Maybe try to think about what she has said to you after work so you are not so bothered by the words. If you think there is areas you could improve on then try to. If you think she is completely out of line start looking for another job. It is very important to be happy at work, but also to be accountable at your job. Line up another job BEFORE you quit if you have any financial obligations.