I had a similar problem with my own DD when she was tiny & I was stumped as I was EBF too, she had the allergy tests & all clear - nothing the doctors gave worked & nothing else we did worked enough, I feel for you, as it was really awful as you just feel so totally helpless when they look so sore & nothing you or the doctors do really helps :( - in fact in my DDs case the creams the Doctor prescribed would often make it worse
Thankfully I have an old friend who works in alternative medicine, specialising in DCs, I don't see her often, but when I spoke with her she suggested it was something I was eating & DD was getting it through EBF - I eat a healthy process food free diet, but we worked out that my monthly cravings for cheap jelly sweets was the cause -
Turned my DD is intolerant to chemical food additives - - google Azo Dyes & Benzoate preservatives, & read the list of chemical additives/E numbers & the effects they can have - you'll be surprised - these can also be found in soaps, shampoos, & even medicines & creams aimed at kids - my DD can't have Calpol for example & the reason the GPs cream made things worse, was the preservative in it - my own DD is also intolerant to artificial sweeteners, they affect her stomach badly, so something to bare in mind if any tummy upsets too.
Intolerance doesn't show up in any tests, medical or otherwise, but is usually easily pin pointed with an exclusion diet. Thankfully these days ( my DD is now 10) it's much easier to find foods that don't contain these chemicals, it's just about reading labels & learning what brands are okay & not all E numbers are bad, many are natural & perfectly safe & many are labelled not artificial additives, though take care, some that advertise no artificial colours, still contain benzoate preservatives or sweeteners, which is a big bug bear of mine
As for soothing the sore rash, I've found adding Epsom salts, lavender aromatherapy oil, manuka honey & oats (tied up in a Muslim bag to prevent mess) to her bath helped a lot , or as its her face mix up a small amount to dponge her face & I even made up a lotion using the same that helped, though you can buy Pure Potions in health shops, which is similar & we find good, though Derma Spray is better but not until 12 months plus. & Sausage Tree cream - aka Zambesi Botanicus is a natural steroid cream that works better than the GP one, without the additives.
My own DD is still intolerant, but her skin is beautiful - unless she eats something she shouldn't of course & then she will have a sore rash flare up within 20 minutes.
HTH