Can my husband really not realize when I need help with our newborn baby?

My husband and I have a 2.5 week old baby and I’m exhausted because I’m breastfeeding and baby eats every few hours. My husband went back to work last week so we decided it’s best if I sleep in the living room with our baby so I can wake up with him and feed/change/put him to bed without waking up my husband because our baby cries when we change him and feed him (getting better but dealing with latch issues). It’s fine by me bc it’s more convenient for me to be in the living room for all that. But I’m definitely a bit resentful bc he’s able to sleep for over 9 hours/night and I get like 3-4/night.

So baby has diaper rash and being new parents we don’t know what to do. So I was breastfeeding and googling and trying to figure out the cause and what to use to treat it. Meanwhile my husband is on his phone and playing guitar. Fine, the baby likes the guitar. But then I changed him and was airing his butt out and started doing diaper free tummy time to air it out more. After a while I went to put the diaper cream on his butt and put his diaper on. Baby started crying hysterically and the cream was going off my finger and getting all over him. Then he started peeing and I just looked at my husband who was sitting above us just looking at us playing the guitar. I said something like ‘it’s fine I don’t need help’ or something rude like that bc clearly I was struggling and needed help. To me, anyone could see that. How is it not obvious that I need help putting medicated cream on and diapering our crying baby? So he got SUPER upset and said I need to ask him for help not just assume he knows I need help. I’m sick of this excuse bc it’s with everything, house chores and baby stuff. Why am I the keeper of chores? I’ve told him many times to simply look around and see what needs to be done and just do it. But he ‘doesn’t see’ it.

He said if I keep going from being perfectly fine to lashing out at him, he’s going to ‘run away’ from me. I said okay see you later. I’m so sleep deprived that I have no patience for it anymore. He said we needed to talk about this issue and I said I actually don’t have time because I need to look up how to treat this diaper rash bc we clearly have no idea since it’s getting worse. Not once did he think to help me look it up, it’s all my job.

Am I wrong here? Is my husband a dud? I wish the parenting was more 50/50 and I do try to involve him by giving him alone time with our baby after work and encouraging their bond. Is this just what it’s like with a newborn?

He left to go food shopping and I started crying thinking how guilty I feel for bringing this new little baby into the world to parents who can’t even get along. My parents are divorced and I thought my life would be different and it would be better for my son but maybe i was wrong.