if you are not eating, yes, your period could bne off. you should eat... soda is empty calories, which gives you a rush at first but weres off fast. if you are trying to lose weight, eat healthy fruits and veggies and real food... soda will not help you at all and is VERY BAD FOR YOU!!! that is why you feel so terrible.
once you get on a normal diet, your period will get back to normal probebly. if it does not, call doctor.