Do you have to confess sins publicly in church or secretly in prayer?

You have to do what Matthew chapter 18 verse 15 tells you.

The first thing you have to do is confess the sin to God then you have to go to the person that you send against and you have to confess that you send against them ask them to forgive you and offer to them restitution for what you have done

Confess to a priest.

bluebell -- "None of those words makes" --  A "rational human being" knows "words" is a countable noun.  So none of those words makE" sense.

You can confess privately in prayer, but to make a sacramentally effective confession you should confess privately to a priest. Public confession is not a normal requirement. 

Depends upon how public the offense is.

I don't "have to" "confess" "sins" at all. None of those words makes any sense to a rational human being.