Relationship issues - am I overreacting or within reason to be upset?

I don't know if I'm overreacting, being too sensitive, or within my rights here, so I wanted to seek out opinions from others.

I have a week old baby and am a first time mother. Overall, I think I'm doing good. I know it's a learning curve but I think I'm doing pretty well. My partner apparently has other opinions and is really starting to hurt my feelings.

I am the one doing 90% of the work. His job refuses time off, so he sleeps at night (yes even through a crying baby) and I am up ALL night with the baby - feeding, changing and soothing. Then, during the day, he is at work and I am left up taking care of the house (lots of extra laundry now that baby's home obviously). I don't really get to sleep when baby does because I'm doing all the housework too. Baby has their days and nights mixed up so that adds to the issue.

He has been nitpicking on me left and right. He scolded me for forgetting to clean the dryer vent (not usual for me at all). He tells me to hurry up and move quicker when I'm doing a diaper change. The most recent one we were giving baby a bath and had a couple visitors over to see the baby. He literally blurts out in front of our company that I need to clean baby's butt better during changes because it's dirty (baby had farted just before bath time and it was... "wet" which explained the tiny amount of "mess"). I felt embarrassed and offended like he was saying I half-as*ed stuff and wasn't a good enough mom. I told him I knew how to wipe a baby's butt. I was visibly annoyed and so he blurts out in front of company asking if I'm mad. I didn't say anything because I didn't want to do that in front of company.

Later he came to me visibly annoyed and asked why I was all mad. I told him I hadn't appreciated the attack on me. He said I was being ridiculous because he hadn't meant it that way. I cried and he ended up apologizing to me several times. He told me I was a good mom and he never meant to hurt my feelings.

Updates
1 y
He said he forgot the baby had farted and that was why they had a slightly dirty butt. I told him it wasn't acceptable to make comments like he did in front of guests because that seems to paint me in a negative light and I don't want people thinking I'm a sucky mom. He said no one thought that. The one guest that was there got told about how I was feeling and they came and talked to me and told me I was definitely not a bad mom.
Updates
1 y
It just upset me especially on top of the other nitpicking. He doesn't even do as much to help. He sleeps while I take care of the baby. Then he works while I do the housekeeping and take care of the baby during the day. I've had basically no sleep since coming home with baby. I've had a few 1-2 hour cat naps here and there but no actual quality sleep. I'm a first time mom trying my best and just felt really attacked by him. Was I overreacting or was my reaction acceptable?
Relationship issues - am I overreacting or within reason to be upset?
Post Opinion