You clearly don’t have mental illness or a drug addiction. Yes, absolutely, you are severely discriminated against with either of those. People see you as utterly unreliable, weak, and unworthy of the kinds of respect afforded to able minded people.
It doesn't matter what they tell you about confidentiality. Just get the care you need through your insurance and avoid the potential honeypot.
Edit: This comment is heavily biased towards an American audience where at will employment, and health insurance rather than government benefit, are the norm.
[edit] Ok, got it. I don't mean to question anyone's personal experience, and sorry that this is what's happening to you.
Also, I don't want to 'rank' the degree of marginalization different groups experience, that's not at all what I'm after. Ideally, none of this would exist and everyone would just live happily ever after.
What I mean is that I don't see a national debate, through politicians or 'celebrities', that deny the existence of, say, alcoholism.
But again, I don't mean to imply that those groups don't suffer. Also, I can just be wrong.