Wind, unsettled, feeds more than any other infant anyone knows, cries a lot, sick a LOT- yep, I know your pain!
My DS was exactly as you describe: his body was / is unable to cope with the proteins in cows milk. It is fairly common, and different to lactose intolerance . DS was breastfed and never had formula, but the proteins came through my milk from my diet. ( this is less usual, we wee unlucky!)
With my DS, the cows milk protein intolerance (cmpi) gave him reflux, he was copiously sick ALL the time, and basically screamed whenever he wasn't being fed. And he fed near continuously, 24hrs a day, or so it felt...
( I was told months later that the breastmilk acts like a mild antacid so they want to feed all the time to stop the pain from the acid in their throats / stomachs.)
It was utter, utter hell, I do feel for you. The health visitor eventually referred us to a paediatric dietician and we were sorted out but only after 5 months of non-sleeping, screaming, vomit-covered inconsolable hell.
Maybe suggest to your HV or GP that your DD might have reflux, and what do they think about the possibility of her having a problem with cows milk? We were fobbed of for months with "yes, yes, all babies posset, it isn't as bad as you think, all babies fuss," etc but we were listened to in the end.
Assuming you intend to keep breastfeeding: it is actually pretty easy to cut cows milk products out of your diet, takes a bit of getting used to and you need to avoid "hidden" dairy such as whey powder in packet foods, and start eating things like hummus to keep up your calcium intake, but it is ok! Do seek advice from a health professional, though, as its a bad idea to cut out while food groups without proper medical guidance.
The bottle-feeding alternative for CMPI babies is a special formula that can only be bought on prescription (and I gather tastes unspeakably vile) so if you decide to switch to formula, maybe speak to your gp?
There is an "allergies" board on here that has lots of knowledgeable people on it if your DD has CMPI. I lurked there a lot when my DS was tiny.
This is very rambling sorry, but hope it makes some sense... You aren't alone in your suffering!