You poor thing: that sounds horrible.
When you say he doesn't like being swaddled, do you mean he fights it when you try to swaddle him? Most babies at this age do fight when you wrap them up, but still sleep better. It's often a few weeks before they welcome being wrapped up. (Although of course, some babies really don't like it.)
Do you have a sling? Try popping baby in it and going for a walk. Slings often work for the most difficult babies. If you've not got one, try putting him on your shoulder and walking around, or rocking with him in a rocking chair / on a birth ball / in your arms / dancing with him. Try any of these from 45-60 mins after he wakes up. He may prefer being on his stomach / side / upright rather than on his back.
A pram or car ride may do the trick.
None of these will allow you to sleep, but you could ask your DH to help (assuming he's on paternity leave), and anything you can do to help him sleep a bit will help him find it easier to go to sleep. When babies become very overtired they find it extra hard to drop off.
White noise may help, as may singing to him.
Harvey Karp's 5 Ss technique is great at dealing with crying or sleepless babies: see video here. There is a DVD you can get, and a book.
Sending sympathy and chocolate.