Oh OP, I had one of these type of babies so I understand how you are feeling xx
You mention you have gone dairy free but you don’t say whether your baby’s formula is also dairy free?
There’s no point you going dairy free if she’s having formula that’s made from dairy?
I had to go dairy free for just over a year when I was breastfeeding DS2 and it was so hard, I felt drained and exhausted for about 3-4 months until me and my body adjusted to it. My point is to just make sure you being free dairy free is essential as unnecessarily removing that food group may be adding to how you feel.
On the other hand, her symptoms could suggest an allergy and if that is the case then you need her formula changed if she isn’t already on a dairy free one.
And I don’t know if it will make you feel better, but the majority of 9 week old babies can’t go over 4 hours without a feed so that’s just a normal part of having a newborn.
Have you considered talking to an IBCLC about how you are feeling? They are educated in the nutritional needs of ex-prem babies and NICU babies so they may be able to offer you some really good practical and emotional support on how beat to juggle all these demands on you. I know people keep telling you to stop pumping but I haven’t actually seen you say anywhere that that’s what you want to do? If stopping giving breast milk is something you are happy to do then by all means it may really help your state of mind to fully formula feed, but if stopping giving EBM is not something you want to do then seeking out the help of an IBCLC may be really beneficial as they can help guide you in finding a way to make pumping and feeding seem less overwhelming and reassure you how good are you doing even if you feel like you aren’t.
I’m really sorry you are having a difficult time and if you don’t feel the mental health care is helping you then I would go back to your GP.