Starting a new job can be anxiety producing even for people who don't struggle with depression and anxiety on a daily basis.
Also know (and I've been more or less constantly employed for almost 20 years) that everyone makes mistakes, especially when they're starting out. It's okay. It happens. As long as you're trying your best to learn the ropes you should be fine.
I'll be keeping my fingers crossed for you

But I have a feeling you're going to do great.