If you breakdown---go ahead! It is your Dr! He has seen many I am sure...it is better to be straight with him about your addiction and get his help, than die from your addiction alone. You can do this---do it for you!
As far as how mine went---it was fine just fine, they understood and was ready to help me win this battle, good luck!!
I've not had to confess to doing drugs, but when I needed to go to the doctors, I also knew I was going to breakdown........and I did. Luckily, I'd made of note of all I needed to tell him. They are doctors - I'm sure they've dealt with many others that breakdown. A pen's also handy if like me, you may be too busy crying to take in everthing he says. Good luck.