While there's no allotted day that people can spread all their secrets, we found a reference to World Communications Day, celebrated each year on the Sunday before Pentecost and was formally celebrated on 8 May 2016.
Another unofficial holiday, which you might be interested in is the Tell a Fairy Tale Day - encouraging celebrators to read, tell, and listen to fairy tales from around the world.
Tell a Fairy Tale Day is on February 26.
Check out a list of fun, wacky and trivial holidays all year round on Timeanddate.com.
Tip! Before confessing your deep dark secrets, Oprah.com offers tips on who to turn to, when to tell—and when to zip it up.