Can I get therapy without my parents knowing?

To the psychologist without the parents' knowledge? Help !

Hello, I'm a 14 year old girl and I'll be 15 in a few days.
Now to my problem: Since the death of my grandmother (2014) I got less and less joy in life, I hurt myself and cried all night. In the meantime I have come to terms with the fact that it is no longer there because I can no longer change it.
Nevertheless, these negative thoughts remained, I am still very often sad, have down phases and just lie around for hours and do nothing because I have no strength to do so. Falling asleep in the evening and getting up in the morning is a torture for me. I have often toyed with the idea of ‚Äč‚Äčkilling myself to make it all end. I've lost some important people and the memories of the bullying in elementary school keep coming back.
In addition, it is very difficult for me to react appropriately in social situations. I'm always too shy, hardly speak because I don't want to say anything wrong. I sometimes feel uncomfortable with my friends. For me, there is nothing worse than being the center of attention or speaking in front of many people (e.g. in front of the class at a lecture). I avoid these situations as much as possible, and I also don't like going to parties and the like. I also feel very uncomfortable when I go out (among people), alone or with someone else. I don't know how to move so that others don't think anything stupid of me. I can barely look them in the eye during a conversation with strangers.
In addition, I started losing weight in November 2016. I was never the fattest in the class and never actually found myself fat, but at some point I said to myself "You have gotten really fat and you always eat so much, your friends are all so thin and just thin Girls are loved. " I then got more and more into it and eventually got around to eating as little as possible. I exercise every day and count my calories. I am now underweight and still find myself too fat.
It's not really normal anymore, I'd like to talk to a psychologist about it.
Is that possible without the parents' knowledge? (am privately insured)
How much is it ?
What do I have to take with my health insurance card for the visit? (then my parents will see that)
Does the psychologist have a duty of confidentiality?
I would just like to know whether this is still normal, whether it has something to do with a pubertal phase, whether it is all just a phase in general or whether I am really mentally ill. On this point I just want to be certain that I am not going into anything.

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