Oh livvy poor, poor you. You sound just like I did with DS1. I just want to give you a huge hug and tell you it will get better, it will , and one day you will discover you are even enjoying it. It's so hard to imagine now, and I remember the feeling of my life crashing down round my ears and utter hopelessness. Your life is not going to be like this forever. I promise.
Being tired makes everything worse. So the way the world looks now isn't a true representation. And it's so hard to cope with the cause of your exhaustion when it's screaming at you constantly. I remember it so vividly and my heart really goes out to you. Keep using the maternity nurse as much as you possibly can. Any friends you have, any at all. Please don't be afraid to put yourself out there and get help Honestly it doesn't have to be so awful.
Maybe consider going to your GP and being honest about how things are at the moment. It sounds to me that maybe you do have PND now, maybe you don't, but you're on the verge, iykwim. If you get a moment, take this online test and see what it looks like. It's obviously no formal diagnosis but I think it's a good indicator.
But really truly and honestly you will enjoy your baby and your life one day. I thought my life was over as I knew it, and I would never find myself again and life was just going to be awful. It's not. My DS1 is the light of my life, and (until DS2 was born!!) I had time to myself, got enough sleep, had so much fun with DS1, went out on nights out with DH - life was life again.
This newborn phase is over reasonably quickly, in the grand scheme of things, but if you have PND and it goes untreated, your feelings could last longer than they need to. I suffered for over a year because I didn't get help - don't do what I did!! It's very treatable.
Sorry to rant. Hope it's helpful in any way. And a big big big hug for you.