Do I tell my lawyer that I'm guilty of the crime if I want to plead innocent?

A cop said he saw me using air duster then I hit his bumper and left the scene. It's not a felony because of the cost of damage. If I am guilty do I tell my lawyer because I really don't want a second dui on my record for huffing air duster. I told him I am innocent and all he says is that its bullshit (my mom told him I have used duster before)but I can plead either way. What should I do? If I can get out of this dui the first one will be erased from my record after a year.