OP you are as far from a crap mother as could be! You sound absolutely wonderful and caring.
I came here to check updates and read your new post.
Your baby sounds EXACTLY like my DS1. I emphasise so much. It was just so awful watching him in pain.
Looking back is easier, he's now a perfectly happy, healthy 2 year old with zero memory of his newborn troubles. At the time my mum said the same, I know it's so so hard but it's worse for you and baby really won't remember it.
For my DS he did eventually grow out of it as others have said. I'm not sure if it's the same with your DD, DS was breastfed and still sounds the same. He was never diagnosed with reflux although he wasn't being sick, just after crying going on for ages until he could pass wind.
Another thing I did that worked, lay him down on the bed/nappy change for nappy change and use a cotton wool ball with very warm (but obviously safe and comfortable) water and wipe it round his bum. Sounds weird but he used to just toot and toot and then feel much better. Might be worth a go.
I also bed shared, I'm not sure if it made any difference as I have nothing to compare with as also bedshare with current DC.
I think I did get more sleep, he slept in the crook of my arm. But you've said that's not an option which is fine. Do you have a next to me?
Just keep remembering, this too shall pass! Before you know it baby's gut will have matured and this will all be a memory.
The first few months are such a blur and so so difficult especially with a fussy baby but you WILL get through it and it will all get better I promise xxx
Ps - have you got your mum or MIL around/close by? Maybe one could come and take baby for a few hours. Even take baby to their house. I know it might not feel right but remember they've both raised at least one baby each x