The rule of thumb with contraceptive pills is that if you start taking them mid cycle (ie, not at the beginning of a period when you first start them) then you should allow 14 days before you are considered safe.
If you started your pill mid cycle then there is a chance that you could get pregnant if you have unprotected sex within the first 14 days.
However, if you started mid-cycle then the pill will alter your cycle so that your period comes 21 days into the packet - most packets contain 28 days worth and your period comes during the last week.
Wait....what? You started you pill pack on April 6 and had sex on April 15 and suspected your period on April 15? That makes no sence. Birth control pills are normally 21 days of active pills and 7 days inactive pills. If I'm reading this wrong, please clear it up.