I think you had a big part of it with "fake it till you make it." But I do think there may be active ways to get there, too. I think confidence is a big part of the solution, and part of developing confidence might be lightening up on the self-criticism. It's the nature of the business that you will make occassional errors, and while you certainly don't want to be nonchalant, you have to realize that it isn't because you are stupid, or even careless. You would never have gotten this far if you didn't have a lot going for you, and it's probably healthy to remind yourself just how far you've come. Pat yourself on the back at every opportunity. The better your image of yourself, the less the opinions of others will matter.
I think self-evaluation is important, but as necessary as it is to be honest with yourself about your shortcomings, it's just as necessary to be fair. If someone else did the same thing, would you ream them over it, or gently point out the mistake and help them find ways to avoid it in the future? I also think you have to evaluate the criticism you receive from others: first, is it valid? second, are they saying this to help you improve, or just looking to tear you down? In some cases, you may decide that the criticism is valid, but the delivery isn't. So use the useful part, and just blow off the rest. (Ultimately, you'd want to be able to stand up for yourself, but until you get that thicker skin, it might be prudent to avoid anything that might seem defensive. A simple, "Thanks, I'll keep that in mind." ought to suffice, and sends a better message to others--and yourself--than, "Oh, gosh, I'm sorry..."
If you look at my profile, I have just a little more experience than you do--two years and a bit, to be precise. So I can definitely relate. If your experience goes the way mine has, you should soon, if you haven't already, start encountering people newer than you who are looking to you for guidance. Scary, huh? But if you've made it through your first year, you've done something--something big--that they haven't, and here's your chance to help them along. Not long ago, I showed someone how to start an NG. It was, like, my fifth NG, and I'm far from an expert, but it was her first, and I think the experience was of benefit to us both.
Finally, a little anger can be a great motivator. I don't mean lashing out, but a little bit of inward "I'll show them!" can be constructive, if you're careful about it. Determined is good. Reckless is bad. But I'm sure you know that.