I do not feel connected to my one month old

I had my second baby on September 23, 2023.  I felt guilty before even having this baby, because it has just been me and my first born for the past two years. I was always so worried I wouldn’t be able to give my first born the same attention she was used to. Well, now the baby is here, and my firstborn has adjusted just fine. She doesn’t seem bothered by her new sister and actually is very involved and curious about her. But I still feel guilty and I get almost aggravated, anytime the new baby cries or need me and takes away from my time with my first born. I feel awful for feeling this way, but I just truly do not feel connected to my second born. I feel like I am taking care of her out of obligation rather than Desire. I have been severely depressed the past couple of weeks and I wonder if that has something. It’s to the point where I don’t even want to be in the same room as my second born. I blame her for something she has no control over. Again I’m not looking for judgment, because I know how bad it sounds, but surely I’m not the only person to go through this….