Does Plan B Need To Be Taken After Unprotected Intercourse?

i had my period Aug 22-25. started on birth control pills (for the first time ever) on Aug 26. i started another period (light menstrual bleeding) on Sep 3-6. Is this normal? + i had unprotected sex while i was having this second light period (sep 3-6). Do i need to get a Plan-B just in case (since i JUST started the pill and i'm not sure if it's effective yet)