I had that same problem when I started a new job- expecting too much and terrified to make a mistake. What helped was to realistically look at my work compared to others. I noticed that other people do make a lot of mistakes and it's not such a big deal. As long as you're keeping up with the team, you have to accept that that's good enough.
The alternative is that you'll stress yourself out or work yourself to the ground and end up crashing, and then you really won't be of much use to the others.