Why doesn’t he show me affection anymore?

Me and my boyfriend have been together for almost 4years, I have two kids. one with him the other with an ex. We live together, he works nights, I work mornings and I also have class in the mornings.
We also adopted a kitty together recently (I dont think he would have wanted to get a cat if he didn’t want to continue being with me)
Lately things have been a little rocky.. I've accused him of cheating on me. We got into some pretty big fights.. When we fight he ignores me until he's no longer mad (normally til the next day) Then everything is back to normal. Its weird. He claims I nag a lot :/ I dont know if im doing it but I want to stop.. I seriously just want to be a good partner. I want him to want me again. Part of me thinks its his job and he’s exhausted.. his job is really shitty. He sleeps ALL day. Sometimes he's awake when I come home around 1 or 2pm but he's normally going straight to bed. I get in bed with him around 11-12, we dont cuddle anymore.. it’s seriously been weeks.
Maybe I let myself go a little and I plan to start going to the gym and putting more effort into my appearance.
... but its like whats the point if I do and continue to go unnoticed?
In bed I've been the only one to make a move on him in what feels like months. Im kind or tired of it. I want him to do some of the work.. I want him ontop for a change and I want him to make a move on me for once :/. I feel undesirable. How do I talk to him about this lack of sex lack of affection without “nagging” or being annoying or should I accept that our relationship is broken and he's not into me anymore and move on? Im scared if I just give up and stop we will never have sex again or cuddle or anything!
This is seriously the worse feeling in the world I feel like a 35 year old women in a unhappy marriage. (Not that there is anything wrong with being 35.. its just im in my early 20s and i shouldn’t be feeling this way)

anyways I need help and advice tips on how to fix this.

Why doesn’t he show me affection anymore?
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