['I cheated on my math test today. I feel horrible about it.', "Hmm..I think we've all been there one time or another.  Are you going to admit it?", "I'm really not sure. I feel like if I don't, I will never forget about it and continue my life with this rotten feeling."]
Well you certainly don't want that hanging over your head for the rest of your life.  It sounds like you have a good moral outlook on life, I think you have to admit it.
I cheated on my math test today. I felt really bad about it.