There's some great advice on here... You are doing great.
It's so so so hard at this point, it does get better. Because they are nocturnal at the start they feed a lot at night- your milks a better quality at that time. Try to adjust your mind to for now your routine has changed.. once you can accept night time is no longer your restful time it weirdly helps. It honestly doesn't last long but it feels like forever because you're awake so much.
With my 2, I struggled to nap in the day, but when they slept I would rest.. a shower if needed but mainly sitting down, dozing, naff tv, eating! Then I'd go to bed early, whenever he settled as the longer sleep he did was always 8 to 12 or something like that..so if I stayed up until I missed a potential 4 hour chunk.
For people that combi feed, a partner giving a feed at that wake up or at 11ish can again stretch your sleep further. Put your headphones in and leave them to it if you'll do this. If baby isn't at the point of doing a few hours yet, they probably will soon.
Co sleeping really helps..do it safely and it's fine. Baby is so used to being with you he just wants to be close. I really didn't want to co sleep with my children. With my first I spent hours trying to get him into a moses.. lots of stress for me and baby. With my second I kept him with me, double bed just us, no covers near baby, he slept next to me and id rest my hand on him if needed. Gradually I'd move further away from him and then after a while he went into a moses.
I'm waffling now but hope you find something useful in my ramblings 😊