I'm not going to give you a timeline on where it'll get better, because all babies are different. But what I will say is the things never stay the same for long with a baby - and the younger they are the faster things change. So the challenges you're dealing with now may well have gone in a month, and whilst they'll be replaced with new ones, they may be ones you find easier to manage.
I'd also suggest not googling when babies sleep through, in fact, try to banish that from your mind, because there's no answer. For my friends and myself, our range has been 6 weeks to 8 years! But depending on how you're feeding, that's something that can be shared.
I get the feeling that your babies crying in the day is more of the issue, and then you're not getting recovery time at night, which makes the days seem worse.
I can go to your health restaurant GP and try and see if there's anything behind it, if not, wait it out and it will pass. Your baby might be one of those that just doesn't like being a baby!
You'll find your feet. I'm not sure it ever gets easier in reality, but we get more used to it. I'm better able to deal with the curveballs that parenthood throws at us.