In a year it won't matter. If typical, you will be off of your parent's insurance. You'll be able to go to the ER as often as you want in complete discreetness.
But, are your parents really the issue here?
I am an alcoholic and have never been close to needing medical care for my drinking. Something is amiss here. Requiring ER treatment for alcohol consumption is not even close to being a "normal experience." Multiple times?
I am confused as to why you think that the only help you need is physiological. You may not be an alcoholic. I'm not suicidal. But if I decide to play Russian Roulette with a revolver, something is surely amiss. If I were your family, and I passed the time playing Russian Roulette, might you not suggest that I needed help in thinking rationally?
At least being an alcoholic would put a reason to your behavior. Please, get a clue before your parents have to pay for a funeral.
warren