PICA is not uncommon. Unless your doctor is a complete bonehead, I would think he or she has heard of it before and could take the appropriate actions. I know hiding it may make it seem like it doesn't exist, or is no big deal, but that is not thinking in a very realistic manner.
And please, don't start drinking. I drank for three months, all day, every day. Getting over that short intense period HURT.
I guess we'll see you in a couple more months. Hopefully by then you will have seen a doctor. I guess there's a reason that pride is one of the seven deadly sins, in your case quite literally.