As you have said, this is about more than church. There have been times when I have been in public settings and things have come up that made me feel different (as in sad like I have a secret that would make me an outcast if the people there only knew). I have been there.
I go to church and pray to forget my troubles and put it all in God's hands. While I have confessed more on this forum than I should--I have never felt like I need to confess anything at church other than that I have fallen way short in regards to following God's will (we all have). Remember, most people go to church because they recognize that they are not perfect and need "help" in some way. Though some ask for prayers, etc, we don't know the troubles of the people in the other seats with us. We go because we are all looking for acceptance from a higher power.