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.
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.