Maybe one of the first things you and your therapist can talk about is boundaries and how to say directly that you don't wish to talk about your problems or therapy with anyone but your therapist.
When my son was seeing his therapist I told him I would not ask about it other than was it a good session. By telling him that, I could ask and he knew that I wasn't looking for details, just showing interest and concern.
Confidentiality is so important. It's what allows us to be able to be open and honest with our therapists. There is no other way.
I'm sure that's frustrating for your parents. That is for them to deal with; the tension and fear they feel isn't something for you to relieve for them.
Of course they care about you and part of caring about you at this time is to give you room, freedom, and to respect your *needs* that include the need to have confidentiality around your therapy experience.