Congratulations on your new little girl!
My DS3 had some neck and upper back issues. I had sore bleeding nipples, but worse on one side. It was hurting him to stay in one position to feed so the attachment wasn't quite right. We took him to see a good chiro and after 2 visits he was all good no more sore nipples!

Hope you get it sorted soon. Maybe you could ask the nurses if it's possible your DD is a little sore somewhere which is why she doesn't like being tilted horizontally. They might be able to get her checked out while you're in there.

Hopefully someone else posts with more insight than me