Is it post pantrum depression?

So I gave birth to a beautiful baby girl two months ago. Lately I’ve been feeling down and sometimes take it out on my husband. He is working all day so I am on my own with the baby. Problem is I don’t feel like a mother. I feel like a nanny and a milk supplier. Don’t get me wrong , I love this baby to death, but I still don’t feel her like my own kid. I feel like she doesn’t want me too. She will calm on her grandmothers and dad’s arms but I can’t calm her down sometimes.

My husband due to work, will come home late and put her to sleep and that’s it. Will only spend time with us on Sunday. When he will finish work earlier he will prefer to go out with his friends or to the gym. Probably because I will act cold and be really a ***. I am not trying to justify my actions but I am really tired , sleepy and have to wait for him to even take a bath.

Sometimes I am having thought of leaving. Home , town or even the country. Yesterday , I almost accidentally chocked my baby with medicine. Honestly, she would be so much better without me. I am crying every day and talk to her with tears in my eyes. I look like a crazy person. My house, my appearance, my hair, my clothes are a mess. My baby though is always clean. That’s the one thing I seem to get right. But so would a nanny.

Before having the baby, I was scared of myself and my mental health. Is this post pantrum depression? Or is it normal to want to leave because your baby will be better without you? is it normal to cry every single day? Is it normal to not have a connection with your own baby? Is it normal to want her to go to sleep just to feel like a person again just for an hour? Is it normal?