I think the counselor has a duty of care to tell your parents, yes - because of your age. Even if you see a different doctor, I think that they will get your parents involved but you need to see somebody.
When they do inform your parents, at least they will then understand the severity of what's going on with you and not just ignore it like before. You need help with this, it's not fair for you to go on feeling this low without help and support.

xx