Seeking treatment is always a good step. The first session is always about taking notes. In fact that is the reason that the first session is often free and it is not as such a session but an exploration.
You explain why you are there and the psychiatrist / psychologist takes notes and asks questions. You should mention at this point any symptoms, feelings, and your wishes. Your being “happy” is what it is all about, and if you are not happy with your counsellor, then your treatment is likely to face difficulties.
The first session is also about exploring your options with the doctor or counsellor. If you are not happy with them, do consider another one. Being happy with your counsellor is a must if treatment is to be as successful as possible.
Do not worry about what you say, because it will all be confidential. And unless you are an imminent danger to yourself or to others, they will not commit you to a hospital, especially not on a first visit.
Doing new things is always scary but seeking help is always good.