If you were that bad, you wouldn't be posting here with your concerns. You obviously love your DD and want the best for her and being unwell doesn't invalidate that in the slightest. Grab the support that's available and be KIND to yourself OP. This won't be an overnight thing but you will get there.
If it helps, my dad had a breakdown when I was eleven and I have memories of him crying a lot. He always felt bad about that but i genuinely think it taught me to have better empathy. Mum and dad are human and kids find that out eventually.
I ended up having a lot of respect for my dad because he was honest about his issues and we knew they weren't caused by ice. A drink of water and a cuddle would usually help comfort him and I actually still resort to that as my default when someone is crying.
My dad isn't with us anymore, he died in December; but I'd rather have him, mental issues and all, than have lost him as suddenly as we did with no warning.
You're a mum who clearly loves and cares for her daughter, that will ultimately mean more to her than whether you were always on top of your game. It sounds like you have done a lot to shield her from things so that she knows it's not her fault. Please, please be kinder to yourself OP.