It sounds like you hurt this girl's feelings when you teased her. You need to understand why you behaved the way you did. You began your letter to me by saying that she became too close to you and that you don't know what happened to you. Are you saying that you became frightened by the level of closeness?
If this is true, then perhaps you teased her as a way of driving her away from you. Try to understand all the thoughts and feelings that preceded your teasing her. Then work on resolving the issue that you uncover.
If you are, in fact, afraid of getting too close to another find out why. Are you afraid of rejection? Are you afraid of abandonment? Are you afraid of losing yourself if you become too close to someone else? Once you identify the problem, then you will probably need the help of a therapist to heal it.
As for what you should do with the girl. It sounds like you don't want to let her go easily. If this is true, then tell her that you think that you offended her and that you apologize. Tell her that you like her and that you would like to start over with her. If she agrees to try again, tell her that you would like her to promise to tell you the minute you say or do anything that she doesn't like, rather than cut you off.
Keep in mind that you will be in danger of teasing her again when you start to feel too close for comfort. This time around, be vigilant. When you become nervous, telll yourself: beware, you are in danger of teasing as a way of diluting the connection. Then make sure that you sit with the discomfort and resist the temptation to dispel the discomfort by teasing her.
As you identify and resolve the reason behind your fear of being too close, you will find that the urge to tease will dissipate.