I was a week late in starting my new birth control pack and now, on the second week of active pills, i got my period. is everything okay?

Yes ...: ...starting the pills a week late got your hormones out of balance and triggered an early period. I would just keep taking the pills in order, including the fourth week/placebo pills. However, instead of using back-up contraception only for the first cycle, I would use it for the first 2-3 cycles. All should normalize after that. Of course call your doc if further questions. Good wishes:)