And yes, your neighbour could wear earplugs - perhaps she does, perhaps she can't sleep with them in, perhaps she can't get on with them and they hurt her ears, perhaps she is excessively anxious and worries about not hearing a smoke alarm as she lives alone... who knows?
But if she can't wear earplugs then yes, she could move bedrooms, I guess. Why not - someone else has had a baby, and it IS a massive pain in the arse to change your house around, as you've pointed out yourself as you're not going to do it, but it takes a village, right? Perhaps she should be happy to help out a new mum by changing her own living habits...
Or perhaps her other bedroom is below someone else with a noisy toddler/3am shag habit/nocturnal night-shift worker so she's damned if she does, damned if she doesn't.
Anyway, yes, she should probably not live in a flat as she's so sensitive to noise. But presumably she can't afford to live somewhere else.
You are a new mum, you are sleep-deprived, you wish you could just stay in bed near to your baby and get on with pumping because it's a crap job to do and you feel it's important and everyone else should understand and cut you some slack. And I do sympathise with that. But you really are being a bit single-minded and slightly selfish about your family's needs (baby, DH, you) over your neighbour. You have more options than her to control the noise, because you are the one making the noise.