You’ve had lots of suggestions and support so I won’t add more to the list, except to say -
Get someone round you can trust, whether that’s your husband, a friend, a family member, a neighbour or even a paid babysitter.
Have some pumped milk in bottles ready for them in the fridge.
And GO TO BED.
I didn’t really have a ‘village’ when my little one was born, and sadly my family didn’t show up for me in the way I had hoped/anticipated (especially having seen now my parents stepped up for my sister with her children); even when I outright asked for help, which is something I really struggle with, I was told “you just have to get used to it” a lot. 😔 For context, I am disabled and struggle with pain and fatigue and also ended up with an emergency c-section, so I was REALLY struggling when my husband went back to work.
BUT there was one day when my mother came round and took my baby, and told me to go to bed. And I slept. And I felt so much better for it. I was only able to get about 2-3 hours (she hadn’t told me how long she was prepared to stay - turns out it was all day, and I wish I’d known that, but never mind) but that was the biggest chunk I’d had in about six weeks and it helped so so much.
We were lucky that our baby was, for the most part, a fairly decent sleeper and consistently woke around every 3 hours for a feed during the night. They were part bottle, part breast fed as I had issues with my supply.
But part of my sleep problem was that a rather traumatic birth experience left my with a lot of part-partum anxiety, which unfortunately did develop into post natal depression, so my brain just wouldn’t let me switch off to fall asleep. It also takes me a long time to fall asleep, so between the two, I was just barely falling asleep by the time my baby was waking again for their next feed.
Right now, you are at your breaking point and you NEED to sleep. Even if it’s just a few hours in one go. So get that someone you can trust to look after your baby, and GET SOME SLEEP.
And believe me - this doesn’t last forever. You won’t believe me right now, but in a few months you’ll be looking back at this stage and wistfully wishing you could go back to it. Babies grow SO quickly, and your baby will never again be as small as they are right now. It is bittersweet watching them grow. But I promise you, there is light at the end of the tunnel.
Good luck!