It is possible to have a late period. It depends on your body as well. But you also have a chance of being pregnant. Birth control is 99.9% effective. Even while on bc your partner should be using protection so thats why I say you have a chance. If you feel more comfortable, definitely talk to your doctor.
Well at 4 days pregnant you shouldn't miss a period its a new bc so it can throw off your cycle a bit. Yaz you skip periods so spotting between is normal. Also periods are funny things I use bc and I still give myself 3 days either way. If your concerned as your Dr about it and take a test to see.
STOP taking your pill. You need to either wait till you get your period then once it stops restart your pill, having protection for 10 days or go to the doc and have blood test done to confirm your not. Your better of seeing your doc because they can give you advice on when to restart or if your pregnant they can start you on prenatals straight away and help you make your descions ect ect.I got pregnant while on the pill and even though now I'm looking forward to her at the start I was shattered and scared. Just don't freak out and stop taking your pill!