Trust me when I say your baby sounds entirely normal to me - as does how you are feeling. It is such a massive shock to the system when you become a parent and it is not helped by the fsct that most people aren't honest about how crap it can be.
So, firstly, stop feeling guilty. You are allowed to feel resentful of this little person who has disrupted your entire life. You won't feel like this about him forever - the first smile is around the corner and that will help.
Secondly, try to forget about housework if you can. I know that it can feel the only way to keep hold of some normality, but I found that if I went out for the WHOLE day then the house couldn't get more untidy and I didn't use any pots! Take advantage of how portable your baby is and go out and about - take train journeys, go to museums, window shop in the big city - yoiur baby just wants to be with you so go and do some things you want to do. I know you feel too tired but once you are up and out it feels soooo much better.
As for the shower - try to shower before your other half leaves for work. I used to use this time to nap though, so if you don't shower every day so what?
Use the sling all day if you have to - wrap slings are brilliant for holding baby steady whilst you put washing on/cook/iron(!), hoover. I know other people may bang on about the importance of naps in their moses basket but trust me, every baby reaches the ability to be away from their mum at a different time, and yours isn't there yet.
As for co-sleeping, I never fancied it, but did it to get me through the endless nights and now DS refuses to do it, so it is not necessarily setting up bad habits. And every habit can be tackled later when you feel better.
Sleep may not come for a while, but your ability to function without it will kick in soon. If you are breastfeeding it is also worth checking out a website called kellymom to understand why, on some days, they want to feed FOREVER.
I have had two like this, I felt exactly the same as you, and it does get easier I promise.