We have already ushered in the month of Nisan, the month which is called the head of all months, as the Torah calls it Rosh Chodoshim.
The word chodesh (month) the route of the word means new - renewal. The moon has a renewal cycle every 29 1/2 days, which symbolizes renewal. We were given the mitzvah of keeping a lunar (parallel to solar) calendar and making Rosh Chodesh following the renewal of the moon cycle (molad). We were given this mitzvah together with the mitzvohs applying to Pesach, to teach us that no matter what level we have fallen to, we can still return to the light.
R' Avrohom Yehoshua Heshel of Apte says that while searching for chametz, one shall also search his character traits and burn the bad character traits which are similar to Chometz. Just as we are considered adults after the age of 13, so too we wait until the 13th day of nisan when we are prepared to truly fight the yeitzer horah.
What is clear, that we now have 13 days to grow and be properly prepared for true searching and burning of chometz.