Is it normal for your breasts to hurt a week after your period?

Probably, but...: Breast tenderness after your period signals you are producing the hormone estrogen. If there is excessive breast tenderness before, during and after your period then you might be producing too little Progesterone or too much estrogen. Since you are obviuosly concerned, and since this pain is not typical for you, your best advice would be to schedule a visit with your gynecologist soon.