Many things can vary your start date, even if on the pill. Lack of sleep, stress, certain medications and illness can alter your cycle. First, you can take a home urine pregnancy test available at your local pharmacy. If negative, repeat in 5-7 days. If it's still negative, and you have not yet started your period, follow up with your healthcare provider. Keep in mind some periods can be very light, even more so when taking birth control pills. Brown discharge or light spotting may be all you will see. When in doubt, take the urine test, then if needed follow up with your healthcare provider who may want to do blood work.
The same thing happened to me in college, and I remember being quite distressed. In my case, it was my body getting used to the prescription. The important thing to remember is to stay calm, as being stressed only made the wait seem longer. That being said, it is still possible to become pregnant while you're on the pill, especially if you don't follow the directions exactly. So I would take a pregnancy test and, whatever the result, talk to your healthcare professional.
Many things can affect your cycle. I know if I'm completely stressed out, my period may be late showing up to the party and it can definitely be pretty nerve-wracking. Excessive weight gain or loss or even medications you may be taking can mess with your cycle, too. But if you are sexually active and have missed a period, a pregnancy test would be your best option. Then, possibly talk to a healthcare professional.