CBT is a start, but if you can I would get some private talking therapy or ask to be put on a waiting list. It sounds like your emotional needs aren't being met/ have never really been fully met.
I would have been terrified as a child having to be an adult and care for a sibling, and perhaps that terror at caring for a little one is reappearing.
The feelings of not being a good mum could be reappearing from your childhood and having to be a carer without being able to experience childhood yourself. (People faced with being a mum in your situation can sometimes even experience deep rage, that they feel is wrong and which turns into self destruction when they realize they never have had a chance themselves).
You are a good mum if you love your daughter, keep her clothed and fed and with a roof over her head while you try to look after yourself.
Remember on planes with oxygen masks, they say you must wear your own before helping your child with theirs? That is the ultimate role of a parent, to make the environment right for your child. Which means making things right for you. You're in survival mode and don't need to do fancy stuff with your daughter, you're giving her more than many others have had.
You have my utmost respect and admiration for having got this far, with probably, a lot of unacknowledged grief.
If you can't afford a private therapist, ask your MH team about online support as these can be cheaper, but you have to watch out for unregistered counsellors.
Here's a handhold from afar, just believe in yourself for a little bit longer if you can. And I hope your husband starts learning to do more emotional work. That's incredibly hard and something I would definitely discuss with a professional, you need a lot of love right now xxxx