Don't talk about mental illness, just talk about your issues. And be specific in what is bothering you right now and you want help with.

"I feel depressed a lot, and sometimes anxious and I don't quite know who I am sometimes. Right now I am mostly bothered by having trouble getting things done, anything that involves other people is difficult for me because of the anxiety and lack of motivation. That's what I'm primarily seeking help for."

If you're very unspecific - "I have a list of issues that need fixing" - they might indeed send you away; but if you just ask for help with one issue only, while mentioning the rest, they will probably not be scared away and try.