Op I haven't read every single reply sorry.
I had a baby like yours, with no help and a DH who worked away! He actually had sensory problems diagnosed a couple years later so vibrations and white noise were awful for him, hated car seats and the buggy and I didn't have a sling to start with but then when he was an older baby those all became things that helped him settle. You've done the first hardest three months and everything will get easier especially when he starts moving and playing and eating and getting himself into a routine so congratulate yourself for surviving this far.
This sounds crazy from what you've said so far but have you tried swimming? Mine hated the bath, used to scream so much I thought he would break but water babies class was just the happiest 30mins of the week and also ensured a great feed and sleep for the rest of the afternoon and then would just be calmer.
Also this worrying about a nursery or nanny wanting him is just your PND talking, they are professionals and will take it in their stride and unlike you it's not for 24/7 so much easier to deal with.
Get a homestart person to come help you get out and about, the more time out the house you have the happier you'll be.
Also do you have any crèches near by the kind you get in leisure centres or gyms, having an hour here or three hours there so you can have a coffee in peace, go for a walk or even home for a quick nap. They have babies from six or eight weeks and even though my baby would scream most of the time at home when he was in there he would fall asleep or settle in a bouncer happy as anything.
Same with a nursery if you can afford it get a couple half days a week and give yourself time on your own.
When your husband has the baby it's so tempting to clean or cook, unless that's something that makes you happy then don't do it. You guys can live off frozen chopped stuff chucked into a slow cooker or takeaways and ready meals with micro steam veg for a few months. That's your time to sleep, moisturise, walk anything you want so don't faff about with jobs.
Look at the organised mum method for cleaning if you don't have a cleaner it really takes off the pressure to do stuff once you've got the couple jobs for that day done. But if your dh can do them before work even better.
You will feel better once your treatment kicks in, your baby will be easier to deal with soon and you can do this.