I agree, his reaction is not normal, and a bit worrying. His stress will deffo be felt by the baby, who, at this stage, pretty much just needs you.
You need to concentrate on you and baby. Stay in bed, as much naked skin on skin as possible, just take it easy.
Get him to go out and do the shopping. Load the dishwasher. Cook..? Even just make you a stack of nice sandwiches you can just grab whenever.
MAYBE he could take the baby out for a short walk locally IF it isn't too much hassle to get out of the house (stairs etc... just wrestling a coat on a newborn is stressful tbf)... then you can grab a shower - but honestly, if you can't shower as often it really doesn't matter.
Also agree with ditching the expressing. It's not actually great for establishing breastfeeding most quickly and easily - which is the one single thing that will make all the difference to your life! Agree with persevering trying to master side-lying breastfeeding: life-changing (n I didn't master it till my 5th).
I agree with trying DH sleeping in a different room. Even a different house, if there was anyone else who could come and help you out a bit (not necessarily overnight).
I'd come and give you a hand if I could! (Am actually considering becoming a post-natal doula once I'm done with mine.) Whereabouts are you? Lots of hugs. This too shall pass.