Hey Peter,
I have a lot of anxiety too, but took an acting class about a year ago. It was an AMAZING experience - very much fun. I think it's *awesome* that you're pursuing it, and it sounds like you actually have acting work lined up for this month? Did I read that right? That's... really incredible. Isn't it usually hard to get those gigs? I think it speaks well of your talents and abilities that you have something lined up, so maybe it helps a little to know that the people that are hiring you absolutely believe you can do that job, or they wouldn't waste their time (there are plenty of people who try to break into acting, they could have chose any of them, but they didn't - they picked you!)
Are you an extra? Do you have any lines? Even though I'm highly anxious, in my class I realized that if I can really tune in and focus on my scene partner, and take in what they're saying/doing (so that I can let my body react to their non-verbal communication), then the audience and stress seems to disappear. Like, I literally became unaware of the people in the room watching, b/c my entire focus was on the other human in the scene that I was working with. It was a really cool experience (and I'd really like to do more of it!).
I don't know if that helps any. Otherwise, make sure you're taking good care of yourself! Some exercise, gentle stretching, plenty of healthy food and water (and nothing that might throw you off or make you more anxious, like alcohol/drugs). Do your best to get some good sleep before you go in...
I don't know if any of this helps, but I hope so... and wish you the best of luck! It really is a very cool thing to be doing, and if nobody else supports you - screw them! It's your life and you have every right to go after what you want! Good luck!