ashamed to admit this...

My husband and I have had sex once in 2017. 
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I have a three month old baby, my first. Last time we had sex I was heavily pregnant and I agreed to it mostly out of obligation. It was terrible for both of us because I was huge and uncomfortable. And we haven't had sex since, including oral sex. 
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Now with a baby, I don't even want him near me. He has tried to initiate sex a lot, but I reject him every time. It's partially because I'm just not in the mood, and partially because I feel like he doesn't help any around the house and also because he doesn't spend enough time with his son. He's like a second child it feels like - does nothing but adds more work. But unlike a child, he's not helpless just a slob. I feel like I'm falling out of love with him. We feel more like roommates than husband and wife. Any spare minute I get I'm trying to do laundry and keep the house in order, and having to pick up after his socks and messes around the house just makes me mad. 
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Plus, he only spends about an hour per weekday with his son. He doesn't know how to comfort him (3 months old) and doesn't even try. When he cries he just hands him to me. It makes me very sad and angry he doesn't take more of an interest in our baby. 
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I'm so lonely. I've started having romantic dreams about strangers almost every night. Is my relationship doomed?