I suggest you read the book "Psychiatric Justice" by Dr. Szasz, that contains the case histories of patients who allowed themselves to be voluntarily admitted and were never released. I am involved helping a woman right now to get released after such an evaluation.
Depression and anxiety are common at your age. It's part of growing up. I am not so sure why you are so happy about heading for temporary confinement in a mental institution. I suggest, before you head for one you read the books by the late Dr. Thomas Szasz about the problems associated with voluntary mental hospitalization. One of his books was "The Myths of Mental Illness". They may not let you out. I will tell ,you a tale about a delightful brilliant seventeen year female teenager in New York who submitted to voluntary mental observation in a very well known New York facility. She got into problems with the staff and called me to get her out. This would take a while. The security guards pushed her around. She resisted and they charged her with assault. They returned her to the facility. In the meantime she or aggravated and set fire to a wastebasket. They had her arrested for arson! Then she got sentenced to jail! Then she violated her terms of ,probation and became a fugitive! I helped her get away (the statute of limitations is long over).
You do not have to listen to your parents or your shrink to go to a program or continue treatment. Such "voluntary" commitment can forever close many job opportunities to you.
Dr.Szasz wrote several books detailing how "temporary" hospitalization became "permanent", and often lasted for many years. If they assure you this can't happen they lie. Dr. Szasz documented hundreds of such cases.
If someone was suicidal, I would not hesitate to suggest they talk to someone, but for teenage anxiety and depression...that's another story.