Hi, and thanks for your query on eHealth forum!
Usually when you start birth control, you are supposed to either abstain from sex during first 2-3 weeks or use another contraceptive like condom, pull out method etc. So, yes, it is possible that you are pregnant. Please take a pregnancy test and see.
Other than this, sometimes if you have thyroid problems or PCOD, hormonal contraceptive pills can delay your cycles due to hormonal imbalance. Since a confirmed diagnosis cannot be given on net please consult your gynecologist regarding this. Hope this helps. Take care!