This sounds very much like alopecia areata. Sometimes the bald patch can extend and can be a great source of embarrassment and distress. The usual experience with this condition is that the hair grows back but this can take up to 6 months. The new hair may initially be white but it eventually reverts to the normal hair colour. Various creams and lotions can be prescribed to stimulate hair growth but results are mixed. Unfortunately many people become very distressed about the condition and can spend a considerable amount of money on dubious treatments for a condition that generally resolves itself.