Truly, I think some, possibly a lot, of this is from nursing. Are you drinking enough? I often felt like that during nursing years. I think you need to lower your expectations for right now. It is ok to be in a "survival" season. I would focus less on getting things done and more on restoring yourself: hot bath, hot tea, small walk, movie or a good book.
It will not always be this way.
I also think, if possible, getting a helper to give you space to breathe, could really help.
It is hard but when school and relationships are the priority, the house often isn't. It is okay.