I deserve punishment for being so stupid
No you don't. You are human. You live in a capitalist society driven by debt. The companies lending you money have been exploiting you, same as they exploit all of us. They don't care about shame. They don't want to punish you. It's all business to them. You don't owe them anything on a moral level, nothing.
You need help. You matter. Your children need you. Money - pfft. As a PP said, the debt is a symptom. Money is simply ability to do stuff, to make more choices. You've got yourself in a pickle and your choices will be more limited than if you had loads of money, but it's not nearly as bleak as you think. You still have the important things - your kids, and they have you, that's what matters most.
You don't need to pay the interest anymore. You can just repay the debt. You should be latching onto this and jumping for joy - or at least ringing Step Change for advice.
But you're still catastrophising, and that's your depression working on you. Please, speak to someone about it. So many people have depression, it's not at all unusual, you're in good company! Your GP will be treating loads of people with depression at their practice. Please, speak to them.
Although - credit where it's due (not that kind! 
) you did really well to start speaking to your creditors, that's a brilliant step forward, well done.