This is entirely, 100% normal.
Human babies are all essentially "premature" - compared with other mammals and adjusting for size and metabolism etc our pregnancies ought to be much longer - eg remember lots of animals can walk immediately from less than a day old.
The reason for this is our big brains - we have such enormous heads to keep all that cleverness in that babies have to be born after only 9 months in order to have better chances of a safe birth.
People often call the newborn stage the "fourth trimester" - ie the baby's needs are very similar to what they were during pregnancy.
Reach out to your friends and family. I guarantee there are people you know who (as I would be) are aching for a chance to cuddle a newborn and would jump at the chance to help. if you don't ask you won't get as their default assumption will be not to interfere or intrude.
There are lots of different slings. for a newborn a wrap sling or kangaroo pouch style is best. what you need is for someone to come each morning just after you baby has had some milk, and let them pop on a sling and carry the baby around as they potter about, while you get some sleep. if you can just get 3 hours sleep like that each morning, you can probably get through the rest of the day.
this stage will not last forever.
do you live anywhere near a college where basic childcare qualifications, nursery nursing or similar vocational things are offered? in some places you can get a student to come and help out for free as part of their studies, as they are learning about newborns.