I've worked for pay in some capacity since I was in my early teens, so I can't quite relate to your situation. However, I did return to school in my late 20's, and when I graduated, it was almost like starting out.
Frankly, I believe you need to take whatever job is offered, even if it's just a $10 an hour job stocking shelves. Once you take the job, work it like it's the most important job in the world. You will have to swallow your pride IMO because you need some type of work experience to move forward.
You also have additional options. Your state unemployment office may have a job/counseling center. The school you graduated from should also offer employment assistance and perhaps a chance to intern somewhere. Getting out and networking would be a good idea, maybe volunteering somewhere and meeting people, or attending a church if you're a spiritual person etc.
This can be overcome, but it will take some time, and as I've stated, I feel you will probably have to suck it up for a period of time and work a crappy job. But that's life; I'm sure most of us here have worked some really bad jobs for low pay at one time or another.
And well done on 1 year sober.