Don't beat yourself up for making mistakes on the job. I've had my new job for around a month and I'm still making mistakes. Sometimes the mistakes are bigger than others, but everyone makes them, you aren't the only one. I know sometimes it can sure feel like it though!
But keep your head up. It will get better in time. But as said above, the day you stop making mistakes is the day you stop being human. You will always make some small mistakes here and there. But the more comfortable you get in your job, the less they will happen.
I have a task at work that I just hate doing as well, and it can be scary at times too. I've asked for someone else to do it before but my management doesn't take too kindly to the idea. You can always ask though but if you are forced to do it, ask to have someone step through it with you once or so. You can get more of an idea of how to do it so it's not as scary next time. But sometimes those things just take practice over and over again to get over. But you're not the only one. Message me if you ever need anything. Keep your head up!
~Angelica