Ones like impatience, obsession with looks and trouble making friends are examples of flaws within the character. They should be flaws that have real consequences for the character in his or her life and advance the story forward. One of the most annoying things about Mary Sues is how easily everything comes to them: fighting skills, special talents, strong relationships, special powers that appear just in time to save the day, etc. If your character has to struggle and deal with real problems your readers will start to feel for her.  If she does everything perfectly with no real adversity, they'll start to hate her. If you do so, you might as well start a diary as everyone has a different personality and should have to freedom to choose what they want to do, so do not base their decisions on your personal opinions, beliefs etc. This makes the story far more interesting and also makes the writing more of an interesting journey for you, stretching your writing abilities.

Summary:
Give your new character some real flaws. Make things hard for your new character. Avoid making the character show similar traits as your own.