I'm not particularly keen on your title, 'convince me to see a psychiatrist'. Why? Well, to me it comes off like you're trying to pass the buck onto someone else instead of dealing with it responsibly. Don't get me wrong, I understand how uncomfortable it all can be and it is often difficult to navigate through the mess that is the mental health-care system, BUT this is a conclusion that you need to come to on your own because the effort will primarily be yours.
Anyways, if you aren't already familiar, there are psychiatrists, counselors and psychologists. All are bound to nondisclosure agreements. Psychiatrists can prescribe medication while MOST psychologists cannot. Psychiatrists are M.D.s, while psychologists are usually Ph.Ds. I've personally found psychologists to be better suited for therapy-- that's what they do and their solutions are not drug-based. Drugs are helpful, when you need them, but for something like SA it's only part of the equation. If I had to measure how much meds helped me I would say 1/5th-1/3rd, which is nothing to scoff at.
Be prepared to do a lot of work and expect to come across some hard truths. Be prepared to have some difficult days. Be prepared to feel vulnerable so that you can really think deeply about what is causing you misery. Skeptics of therapy look at it and see patients as suckers or chumps b/c the results are not concrete and it's not 'measurable' in the scientific sense. Even though most of us can look to teachers and mentors and accept how much they have changed our lives. Going through therapy is just a different form of education. There are a lot of good people out there.
"Courage is not the absence of fear. It is acting in spite of it." --Mark Twain