First, call your insurance carrier to find out who is in network, and get an idea about the costs.

Second, depending on your situation and how resilient you are, it can take years to undo learned behaviors that were used to survive or cope in your current abusive conditions. A good therapist will help you see that there are other ways to think about the things bothering you and help you develop tools to manage your emotions, set boundaries, and care for your emotional well being.

Third, it can take a while to find a provider you like. Don't be afraid to find a new therapist if you feel like the one you have isn't being helpful.

With respect to your insurance company, the only thing that's going to be on file is the claim from the provider, which will list the diagnosis, and they type of service they provided, (30 minute visit, 60 minute visit.) Your claims, and explanations of benefits are protected by HIPAA law, which means only you, the insurance company, and the provider have a right to have access to those records on file with the insurance company. If your parents attempt to get those records without your permission, (a signed form,) the insurance company and provider will tell them to go fuck themselves, but in a more polite manner.

Your provider might take notes about your sessions, those are protected by HIPAA privacy law. You can expect the things you discuss with your therapist to remain private; HOWEVER, a therapist is a mandated reporter. Laws in all 50 states require a therapist to contact authorities if a patient is a danger to themselves, to others, and/or if the therapist suspects that a known child is being abused.

If your therapist is recommending medication, find a psychiatrist, do not do that shit through a primary care doctor.