If you are definitely taking your pills at the same time everyday and are still having a period you should be okay. No method is 100% so I would recommend if you are concerned to use 2 methods such as a condom and Birth Control pills. If you believe that you could be pregnant, take a home pregnancy test. There actually are pregnant women that do have a type of spotting which seems like a period but that is mostly if the person doesn't have a regular period from the start.
Typically the only ways that that you can get pregnant if you are on birth control: -If you aren't taking the BC at the same time/regularly every day. -If you switch from different forms of birth control (ie: depo prevera(sp?) and birth control pills) -If you are on antibiotics and birth control. Some antibiotics/medications interfere with birth control pills so make sure that you talk to your doctor when going on new meds.
On shows such as "I didn't know I was pregnant," it does show different circumstances that women have become pregnant and not even know it... (such as still having a period and no weight gain). This is REALLY RARE though.