Aww its horrid isn't it but stick it out. My first was like this too. And was on my own also. The only advice that stands out to me is sleep/rest when they sleep. Don't worry about the house. Sometimes I found a lavender bath before bed helpful or a diffuser or oil burner on while you bath baby before "bedtime" x
When my baby is having trouble sleeping, I will put her in the bed with me. I take precautions to follow the sleep safe rules while cosleeping. I also keep her in a sleep sack and no blankets. She sleeps way better next to me
Feel free to inbox me if your awake hun x
This unfortunately is the way it is those first few months I found. They don't have a day night cycle yet. I've found I just needed to roll with it. If my son wouldn't sleep, it was more exhausting to try and get him to sleep than to sing a few songs together. Once he started showing signs of tiredness I would give it another go. You can also start a bedtime routine in the evening and make the room dark during the night and light during the day to encourage development of the day night cycle. Also see if there is family or friends that might be able to help with some household chores so you can care for little one and sleep.