If it was more an intake kind of session, and the caseworker isn't necessarily who you will be seeing, I would give the six weeks a try. This is based on your desire to try a free service first, before attempting an independent therapist for fees.

But try to remember that what you get back from therapy is related directly to what you put into it--they are not mind readers, magicians, or perfect mommies. You mentioned not telling him of your suicidal thoughts; that's an example of something important to illustrate the nature and extent of your depression, and leaving it out might feel safer in the moment, but it does not help you in the long run.

Be as open and honest as you can, and when you feel you are misunderstood or unheard, correct him and tell him what you feel and think. Do your best to stick up for yourself, and even if you can't during a session, write it down afterwards like you told us, and bring it to the next session.

If, after trying that for a few sessions, you don't feel you are being heard, then dump it and go for a paid therapist, if your parents are willing to help.