You've already had some very helpful replies, I just wanted to say that I felt very similarly to you. I am the sort of person who likes being efficient and "doing" - I found it incredibly stressful being pinned down by an almost constantly BF baby and seeing literally hours slipping by without eating, weeing (no need seeing I didn't manage drinks as I should) and particularly jobs going undone day after day. I felt totally removed from the old "can-do" me, I felt I'd never get my life back, it was hard!! I also struggled to get out of the house after a EMCS, and Dc was tongue tied and fed for over 14 hours a day for the first 9 weeks / it can be overwhelming.
You are NOT failing. You are looking after the baby and right now that means a lot of feeds and cuddles - housework and stuff will always be there (alas). But before you know it, your baby will be bigger, will be able to go on a mat to play etc and will feed less and it won't be so intense and demanding.
To reiterate advice from others, some things to help:
Sling (the old Mumsnet favourite) - I couldn't get along with them with my first but was a godsend with baby 2 when juggling newborn and a toddler
Thermos flask - get your DH to make you a hot drink in a thermos mug
Packed lunch / nibbles and Bottles of water etc dotted around wherever you feed so you don't go without.
Wash in the evening (or whenever) your partner is home.
Acceptance: so hard when it's your first, but accept this is what needs to be done for now but also know it's surprisingly temporary
Take any help you can!
Four weeks is not long to come to terms with this monumental change in your life, your body is still healing, be kind to yourself. Good luck and congratulations