As a black woman (without mental illness) who owns a business, I can tell you: You're never going to overcome impostor syndrome until rid yourself of the feeling that you're doing something you shouldn't be, that you're getting something you don't deserve, or that you're cheating others. This is a debilitating mindset that will only exacerbate mental illness.
How do your clients see you--not your potential clients or the wide market out there, but the clients you have worked with? If they see you as their hero, that's who you are to the world, and that's all that matters for the purpose of your brand. Distance yourself from people who think of you as "a black woman with a mental illness." That may be part of you, but it's not part of your brand.
Ask for testimonials and referrals from happy clients. The testimonials will do a lot to alleviate your impostor syndrome, give you a bright picture of what you're capable of, and provide the positive vocabulary you need to describe yourself and your business to start. The referrals will give you the opportunity to repeat successes and build on that confidence.
To build your expertise, start with branding. Formulate a way to express your unique point of view. Not your product or service, but its angle, story, or purpose. Make sure it jibes with the market you're in. It doesn't have to be game changing, but it should get the attention of the people you're interested in working with. No one else matters.
Spread the word about your unique point of view--again, not your service necessarily, just your idea. Elaborate on it and make it a part of your brand. You'll eventually want to publish something (can be a book, but can also be a blog, video series, and/or podcast) that establishes you as the source for this particular approach to your industry's challenges.
Online, this involves engaging on social media. Offline it involves living your unique approach in as much of your business activities as it applies to.
So you'll need to know where to find the people you want to communicate with and how best to convey your ideas. When you find them, build and maintain relationships with them. These people (clients, prospects, fellow industry experts, influencers, and experts in related fields) will become your professional community, consisting of people who value your brand. They're a tremendous source of support whenever you start to get doubtful about your capabilities.
We (not only black women, but all disadvantaged individuals--and even people who aren't disadvantaged but have sabotaged themselves socially or mentally) tend to think we need to meet a bar to prove ourselves first and be successful second. In reality, no one can prove themselves until they're successful.
So if there's something you perceive as a "bar" in the arena you want to play in--be it education, industry experience, network connections, etc.--that you haven't acquired at the level others you admire have, ask yourself: "Have I succeeded (i.e. reached my goals on my timetable) without it so far?" If so, you probably don't need it. If not, you probably still don't need it--you just need to adjust your strategy.
None of the above "bars" stopped others in your position, who worked creatively to achieve their dreams without them. Not saying those things don't matter, just that you shouldn't give up because you don't have them. Remember: your goal is to live your dream, not be recognized for living it.
I'd be happy to take a call if you'd like to work on formulating your brand strategy and authority platform.