J.,
I suffer from anxiety as well. I used to have wicked panic attacks, even.
I started a new job 3 months ago, and have a super intense boss as well. I have spent a lot - way too much- time worrying about my newbie mistakes, feeling sick to my stomach, stressing out about the job.
One of my co-workers suggested a book by Dale Carnegie, which I would recommend to everyone: How to Stop Worrying and Start Living. It is a fantastic read. I love the way he writes, it is full of interesting stories, and it really has solid advice on not only WHY you should stop worrying but HOW you can, as well. I feel that I am already doing much better, thanks to this wonderful book.
It also helps to know that so many other people go through the same thing. Many of my colleagues that I look up to have mentioned how sick to their stomachs they used to feel when they first started doing (fill in the blank). The more you do it, the easier it gets.
Also, a new position takes quite a while to get used to. Give yourself time! While it depends on the job, I would imagine it will be 6 months or more most people feel fully trained and capable on the job.
If you are feeling like you are going down a spiral where you consider self-harm, definitely talk to a doctor. I took Zoloft for about 6 months, when I was thinking about harming myself a few years back. It was amazing how much the medication helped. I was able to wean off after a few months (I think my episode was related to pregnancy hormones) but I am so glad to know it is an option if I ever start feeling that low again.
Good luck to you! Truly- call a doctor, check out that book, and give yourself time. I always tell myself I can't expect perfection of myself. All I can do is be the best I can be, and I really do, and I know that it shows in my work, even though I make mistakes still. It's okay!