Baby is rarely settled. That's part of the problem. My wife and I are both in poor shape right now, for some reasons similar, some different. She has been trying to help me out but even small efforts seem big for her. I am trying to understand. I think i am taking on more than I can handle. I cook every meal, I do the majority of housework, I do all the yard work, and I drop it all whenever she needs something. I am trying to encourage her to do more, but I don't want to put undue stress on her. She has had a hard year. At the same time, I feel like I can't keep up with all my responsibilities. I'm not emotionally overwhelmed, but I am physically overwhelmed. Hers is the opposite problem. I'm sure we are more or less in the same boat as other parents of young children. If we had more than one my world would be some sort of absurd nightmare existence. Just wish the kid would sleep, really. That's the number one thing that is keeping me down. Every hour or two we're still getting up to settle him. He'll be a year old July 12. I hope his sleeping improves soon. He's actually been worse the past two weeks than maybe ever before.
Your situation sounds a little like mine. I'm the one full time with our second kid, and I've found it overwhelming at times. Like full on breakdown. I have other issues that I have to deal with at the same time, and this makes it tough. When my second kid (~ 1 yo) went into their teething phase and upset routines, sleeping, eating etc, it really got to me several times.
His sleep pattern was really rough and was made worse by the fact that I was forced to rock him to sleep (something I learnt from the first one NOT to do - because they learn to rely on YOU as their sleep aid, meaning any time they need to sleep, they need YOU). But circumstances being what they were, there was no other choice (in short my wife left for a couple weeks, and I was trying to manage two kids, with the baby getting weaned from breast feeding cold turkey).
It was rough, getting only 2-3 hours sleep a night, mostly broken up, and even after my wife returned, it has taken a while to settle into anything resembling a routine. with a lot of hard work, we've manage to train him a little to sleep on his own, so that eases things.
He's teething though, which is really rough. Parents with rough tethers know how it is. starts teething so chews on things, but loses appetite and sleep, but is ironically hungry and tired all the time.
I don't have any advice, but to share my own experiences (and it hasn't ended yet!), but rest assured you're not alone. For me, knowing that helps get me through. For you, it does seem you might be pulling more than your fair share of work - and that is always hard to gauge, because "work" in parenting is by its very nature very unbalanced and hard to compare. For women, it usually means waking every few hours, nursing etc. it can be very dangerous for either party to assume their own workload is more "important".
I remember what it was like with our first kid, it seemed rough at the time, but with our second, everything sort of naturally fell into place (and yes, it's tough), because when you're not dealing with baby's stuff, you're dealing with the other kid. It wasn't until our second kid di my wife and I realise what it meant to actually work together as a team., because before, our first child would have two doting parents, and one could rest or get other stuff done. With two, the logistics are exponentially more difficult and demanding.
As for sleep, we utilised a sleep training regime for our first kid...now I don't believe in magic bullets, but all things you research yourself, you pull out what you feel are the important bullet-points and modify to how you feel is most appropriate, but sleep training for us basically involved letting our kid know they didn't need us to go to sleep (and more importantly go BACK to sleep). The idea was to set up a routine that basically was a way of communicating to them that sleep time was coming, and to stick to it. Gradually they get used to the idea, and we modified the routine to start including things that helped, and to remove things that we didn't want.
best of luck.