Only read page one.. there is some merit in what your parents say.
Its true that if you visit your GP and report depression or indeed any sickness be it physical or mental, then it is recorded. Think about your future employment and any circumstances where you may have to declare such illnesses or permit access to your medical records.
Clearly what is going on in your life is unhealthy and needs to be addressed and i think the first step starts with you,some internal conversation,quietening of the mind and some honesty.
You could also initially seek help from voluntary organisations,attend local self help groups and meetings. That way you could make a start on your recovery without it being officially stamped on you.