My 3y/o hits & bites herself?

She starts school this year and so we have been practising writing her letters and numbers. She can write her name perfectly but the rest of the teaching has backfired. She is VERY smart for her age, everyone says so. She is such a sweet girl but has anger problems. She has such a willingness to learn but towards her trying to perfect EVERYTHING she gets so angry. I encourage her so much and insist that she is doing a wonderful job but she never thinks so and starts to punch her other hand repetitively. She will also get very angry when I tell her that she is doing something wrong and bite herself really hard. She also can be playing very nice and be sweet then out of nowhere he mood changes and she is being very DEFIENT, not listening and acting out. She will bug her sister for no reason and cause a fight. I'm not sure if she needs medicine for something or whether to bring her to a psychologist. Can anyone help me and let me know what I should do?