Self preservation (and cat preservation) is the most important thing.
Switch to formula. Express just enough to stop your boobs from exploding. Use earplugs. Sleep. Just sleep.
During in the day, stick DC into a pram contraption, but a coat and good shoes on and walk. Crying doesn't rip through your earholes nearly as much when you're outside and you'll benefit from fresh air. It's more interesting for the DC as well.
Let Dad do more. If you're doing bottles, it'll probably be easier for DC to learn to settle with him first because his instinct will be to root for your boobs at first. Expect some issues at first (and be delighted if he takes to the bottle).
Buy some dummies. They might not be needed, but htey might work brilliantly.
And if it gets too much, remember that the 'oh, they're only little once' isn't just a warning - it's a promise.
Human babies are far more dependent for longer than any other mammal. But even so, they aren't this dependent for much longer. It will get better.
I think babies are cute and defenceless, but ultimately, rather boring. DP adores them. I far prefer them as they become little people - if I want adorable and defenceless, I'd rather have a puppy or kitten.
But you need to protect yourself - hurting an animal is a sign things have gone too far as you are.