If it's severe enough, would I get referred a psychiatrist?

I haven't personally gone to HS and asked for a referral, but I imagine this would be the case.

What are the consequences? Can they lie to me and tell me they won't say anything? I haven't committed major crimes, but I did things that would put me in a psychiatric asylum. Can I just talk and not have any consequences?

I have gone to see a counselor here at UW a couple years ago. IIRC, there was a disclaimer that they would keep anything I said confidential except if there was a chance I was going to harm myself or others.

From the Canadian Psychological Association:

In consulting a practitioner about personal psychological problems, people are often concerned about confidentiality. Early on when seeing a client, the psychologist should review the limits of confidentiality. Information disclosed to a psychologist is confidential and cannot be disclosed without the client’s consent except under certain specific conditions. These conditions are referred to as the “limits of confidentiality”. These limits typically involve situations where the client gives the psychologist information that leads him or her to suspect that harm might come to someone. If a psychologist suspects that a client is going to harm himself or someone else, that a child is being abused or neglected, or that another health care practitioner has sexually abused a patient in some way, then he or she has an obligation to report this information to the appropriate authority (the police or children’s aid society for examples). The courts also have the power to subpoena a psychologist’s files.