Is this PPD or am I just heartless?

This is a hard post to write.

I'm 6 weeks postpartum and I am not enjoying motherhood at all. I can't work out if I'm a heartless bitch who shouldn't have had a baby, or if I might be going through something.

First: the baby was wanted - I even had IVF to conceive her.

However, the pregnancy was rough, ended up with a c-section, baby was in NICU, lost 10% of her weight because I couldn't establish breastfeeding (my milk dried up first week in from the stress of the NICU stay and she wouldn't ever latch). I couldn't carry her at the start because she was nearly 5kg at birth and I was recovering from the section. I never felt that surge of love when she was born or when I finally held her for the first time.

She's a sweet baby. She's formula fed and will sleep 3-5 hours at a time. I do shifts with my partner, so I always get at least 4-5 hours of sleep in one go, plus maybe one nap a day. I eat 3 meals a day, shower daily, have time to clean, relax a bit, and walk the dog. I know this isn't the norm and I'm grateful.

But I just don't enjoy being around her much. I have no desire to cuddle her (though of course I do it anyway), I always find reasons to be out the house solo and I don't miss her when I'm out. I am completely capable of taking care of her, and her needs are met. I do tummy time, sing to her, bathe her, feed her as soon as she fidgets, read to her, walk her in stroller, etc. But I feel nothing if I hear her cry (which is thankfully rare anyway) and don't like doing these activities - it's like doing the dishes.

I don't feel like a mother. When anyone tells me how rewarding motherhood is, I can't relate. It's so monotonous and I hate my new life - which is weird as I was a homebody before and this is no huge change. Baby groups aren't useful because I don't feel anything like the other mums do - I feel like a fraud.

I have a year of maternity leave from work, and I'm already considering trying to go back at 6 months. I've already decided I never want another child, and even though I've gone through infertility, I am researching getting my tubes tied.

I don't know what's wrong with me. I feel completely empty and disconnected and flat. It's not even like I cry, I just feel like a ghost floating around my life. I've concerned she'll pick up on my lack of maternal feelings and end up hating me or feeling sad. Part of me wants to walk away from my life entirely, I think her and my partner would be better off without me.

Can anyone relate? I have my postpartum check up soon and I'm not sure if I should tell them this. I'm worried I'll be judged / have social services visit me. No one has flagged anything yet, but I've never explained how I feel.

Edit: I would NEVER harm her. I am not feeling angry or out of control. I'd never let anyone hurt her.

Edit 2: Thank you to everyone who took the time to read through my post, share their experiences and give advice. I've read every single comment and appreciate your wisdom, and it was especially interesting to hear from other IVF/NICU mothers. I feel less alone and less like an alien after hearing this isn't totally unheard of. I'm so happy to hear most of you found peace and happiness with your babies over time. I will mention how I'm feeling at my next check-up appointment. I'm not in the U.K. or North America, so the healthcare system is a little different here, but I'm sure there is help to be found somewhere.

I also agree I may have incurred trauma after trauma with the infertility, IVF, bad pregnancy (severe polyhydramnios and risk of her dying if I had a cord prolapse), sudden c-section, NICU stay, and then my milk drying up and losing the chance to breastfeed. Typing it out, I can see it actually is a lot of stuff. I'm not in touch with my parents and I live abroad from my home country, so I've been keeping all of this deep inside. The only person I told was a health visitor (the part about the bad birth and immediate post-natal experience) and she told me to move on and put it behind me and focus on the now. The next one just spent the hour trying to get baby to breastfeed even though we were formula established by that point and my milk was long gone. In hindsight, that put me off asking for help or sharing how I feel - the health professionals only seemed to care about how I was feeding baby - and being clear it should be breast milk only - and nothing more.