Sleep deprivation is hard. Unfortunately I don't have a miracle cure but I can tell you that both my DDs slept best when in sleeping bags that kept them in. We used wrap me ups (I think they're now called love to dream). I found that when I was wrapping only they would get their arms out and wake themselves up. They couldn't do that in the bags

As for how to cope, I think the first step is making yourself feel a little better. For me, everything always seems even worse than it is when I'm extremely tired (not saying what you're going through isn't bad, but it might be being made even worse due to the extreme tiredness). Since DS is taking formula, could you have someone watch DS for you one night? I would have this happen in a different house to you, so DS goes somewhere or you go somewhere else to try and reduce your anxiety and hearing him all night.

As for the long term, my first suggestion would be to stop trying to get things done during the day for the time-being. I know this is hard. I myself am one of those people who try to do everything with a new baby, but its truly not worth it. For now rest when he does. Even if you can't sleep, sit or maybe lie down. Recruit people to do things for you or, if you want to do things yourself, have them come during DS's cranky times and have them hold DS whilst you do stuff then, as you wouldn't be sleeping or resting then anyway.

Good luck! Please know this doesn't last forever, even if it does feel it at the time.