Please don't think for one minute that your dad will be anything but bursting with pride for you
In your OP you mention you have depression. Are you getting any help for this? I can totally empathise with the feeling of self loathing, ive been there - i am often in that place and its pretty shit isn't it. I am on medication and im in counselling, about to get some CBT therapy as well.
I think you need to go and talk to your doctor, TOMORROW, please? You cannot go on this route of self destruction. Ive done the screaming at DD thing too, and like you, felt awful - I daresay my DD doesn't remember. She loves me and needs me. Sometimes i thnk im a shit parent - but im not. Neither are you.
I'm worried for you, I don't like your nickname - you are NOT a loon. You have had a lot to deal with, it has to come out somewhere - you sound a very strong and brave lady actually - that took courage to leave your ex partner, something that i think your father would actually be very proud of. Seriously, any parent would want their child to be able to be happy and not be abused in any way within a relationship.
I can totally understand the kitchen thing too, i suffer from extreme anxiety and whenever i am anxious i am almost paralysed by it, you can guage my mental state by the state of my house. But you know, whenever i pick up, i clean up - it is doable. Just do it when you are ready. Do you have a dishwasher? If so, just load it as you feel like it - or just set yourself the task of emptying it for now. Then you can fill it up as and when. If you don't then fill a bowl of water, shove some washing liquid in, stick a pile of plates in there. Leave it, go for a walk, have a cup of tea, whatever - then wash and rinse them. If that spurs you to do the rest - fantastic - if not. Well, youve made a start.
Please go to the doctors. I have posted very similarly to this in the past - its horrible to feel like this - but you don't have to. This could be PND, i had this and it wasn't diagnosed til DD was 2.
Stop being so hard on yourself. Try and get some sleep - make sure you get out of the house tomorrow and keep posting.