it depends on what your parents are like, but if in doubt the best thing to do is be blunt with them. if you're going to the emergency room then they're probably gonna find out anyway, at least they hear it from you. if they look like they're going to fob you off, just be firm, if you have scars show them, if not then just keep on being insistant, I mean even if they're not sure theres no harm in them going just in case right?
Yes, you go to the reception desk they will ask your name and what you have come in with you can write it down if you want to be discreet. You will wait in the waiting area for a little while and a nurse will triage you, tell her about your feelings, what's going through your mind. You will have a little wait where you will see a doctor, he/she will take a more detailed history. To get the help you want you have to be as honest as you possibly can. They will then refer you to a mental health liason team who will do an assessment of your mental health. They will then decide if you urgently need a psychiatrist and can refer you to other services such as therapy. I did this not long ago, it's not as scary as it seems.