You may say, for example:

"During this visit, I’ll ask you some very personal questions to best help you. I promise that whatever you say will be kept private between us, and not be passed along to your parents or anybody else outside this office, unless you give permission.”

Clinicians may end the introduction with:

“The only exception would be in a circumstance in which a disclosure to someone is required by law.” 

Other clinicians prefer a non-qualified ending:

“If you tell me something that is so bad for your health that I think it is best to get somebody else involved in your care, like a parent or another doctor, I will tell you that. If you disagree, then together we can discuss the way to proceed.”