Hey so I don't really have much advice for you...but when I read your post it made me think of me. I was in the same position just a couple months ago. I knew I had to talk to a therapist but didn't know how to tell my parents. I thought they would look down upon me but eventaully they found out I was depressed and talked to me about it and were surprisingly very supportive about everything. So if I were you I would just stick it out and tell them that you are having trouble dealing with some things in your life right now and you think talking to a therapist would benefit you.

Sorry if that didn't help at all.

Feel free to PM me if you ever need to talk