I don't think you're too sensitive at all. Of course, he is tired from work, whatever that might be, but being on maternity leave isn't a holiday. You look after your baby and that's both exhausting and rewarding. It might be best to have a chat with him about how you're feeling. I also think it is normal for sleep deprived parents to sometimes argue about who is more tired or has done more. Maybe you both need a bit of a break. Do you have someone who can look after your little one for a few hours, so you can have some time for just the two of you?
You're not being too sensitive. Your feelings are valid. Men just simply doesn't seem to understand. Have you tried talking to him? About how you feel and how your day to day is? Also if he works from home- I guess it's by a computer? He really shouldn't be complaining 🤨