Does he fall asleep after eating? Hold him upright to let burps naturally escape without GERD/reflux. Some babies like to be 90 degrees at almost all times and even being at an angle of 45 will not do for them. Some like to be horizontal and feed lying next to you or the football hold.
One lady who was a baby expert said most babies need either vertical or horizontal to the person holding them and the floor and that's that. Find out which seems to make that baby happy and stick with it. Maybe use a baby carrier worn on the front in order to do dishes, etc.
Heck I had to cook with my daughter in a front pack. Talk about scary. I had to stand away from the stove and cook easy things. She was a "has to be upright" baby and so was my next one.
Babies have a weak esophagus and reflux is often an issue without food sensitivity. This reflux in an already "has to be upright" baby compounds the need to keep them upright and feed tiny meals frequently, like a max of 4 oz. every 2 hours. Seriously, feed them like a tiny bird. They have a delicate digestive system.
Yes, you need sleep. Poor you.
My first was the same.
The front pack was needed for a month, then the baby swing when she was older, allowed me to get basic food prep and wash done. I even had to sit and watch TV with her on my chest, upright.
I was very tired.
She also didn't want anyone else, not her dad, nobody. They can smell mom and that's all they want.
Most new mom's feel how you feel. It is not an easy right of passage. Nobody tells you how hard it was for them because they hope you will luck out and get an 'easy baby.'