First I'd like to extend a warm welcome to the BB forums. I hope you will find some support here.
Well done on graduating uni! I know how tough study can be when you are also struggling with depression so it is a huge achievement that you were able to complete your degree.
Leaving uni and moving home is a really big change. It will probably take some time for you to adjust. It's not easy to make new friends with social anxiety, but since you have made friends in the past so you know its not impossible.
I understand that finding work is tough at the moment (I'm also job searching) and it can also play a big part on our mental health. It's hard not to feel worthless when you don't get interviews or in some cases even replies from job applications.
It's important to remember that there are likely literally hundreds of people applying for each job at the moment and many of them have the same skill levels. You haven't mentioned your field, but is there the option of getting an agency to help you find work? Temp agencies also help people find permanent positions and a lot more companies are outsourcing their recruitment now days.
Have you spoken to your GP or health professional about your mental health since you moved back home? You might find some psychologist counselling or going back on medication will help get you through this tough time.
kind thoughts, Jess