SashaSays. I'm sorry to hear that 🙁 Is that since you had DD or did you suffer from anxiety beforehand?
I agree with RedCrab that part of it is the full responsibility for the baby when you parent alone.
You need to see a different GP. Whether it's meds or therapy etc there are things that can help. Don't take 'no' for an answer, you don't need to live like this, it's miserable.
Are you going to any baby groups etc. It'll help if you make some 'Mum friends' and you'll also learn how many 'oh fuck' things are perfectly normal, how not all babies sleep through, how normal it is to feel tired & fed up sometimes. You are parenting your DD on your own, but you don't need to do it in isolation iyswim.
You are far, far, far, from The Worst Mum or a Bad Mum. Babies routinely fall from sofas & beds as you can see 😊
DD will be fine with you as her Mum! It's you I'm worried about. See another, more clued up, GP 💐