Hugs to you.

I can't tell you what you "should" do but I will tell you what I would do in that situation -

It sounds as though your parents are pretty supportive so if I had that situation I would tell them I wanted to see a therapist. You don't have to explain in detail to your parents why unless that is something you want to talk about. If you are comfortable discussing your feelings with your parents then do it but if you are not comfortable tell them you would like to wait until you have had some counselling with your therapist because right now talking is uncomfortable. I don't know the situation so I am not certain.

There are some friends that I have told about seeing a therapist. Very few of them know why. If you have some close friends that would support you then perhaps you could talk to them. I am not a very trusting person so I like to keep my life private from nearly everybody but as I said, I am not you, so I can't really advise but only tell you what works for me.

Good luck and if you need to talk I have found this site better because there are people with similar problems that relate to me better than most people that I know where I live.