ER visit, dehydration and now formula!

On Sunday evening my husband and I took our almost 7 month old to the ER as she had been throwing up all day and hadn’t had a wet diaper in more than 24 hours. Once there they checked her weight, temp and stuck her 12 times trying to get an IV in her. They finally found a vein in her ankle and began giving her fluids. They ran blood tests and did a urine culture all to come back and tell us she likely had a stomach bug and all we could do was give her pedialite and cuddles. We were upset and frustrated after such an ordeal and simply just want our daughter to feel better. We went back home, did what they said and went in today (Tuesday) for a follow up with a pediatrician. At the ER she weighed 11 lbs and at this visit she weighed 11.5. The last time she was seen was at 5 months where she weighed 12.5 lbs. Given that she has been sick for the past few days my husband and I expected her to have lost some weight but the pediatrician acted as if we haven’t been feeding her at all even before she was sick saying “she is very tiny for babies her age, are you sure you are feeding her enough?” I am exclusively breastfeeding and I do not pump as she won’t take bottles at all so I have no measurable amount to tell her but I simply stated “she feeds on demand and normally has enough wet and poop diapers as any normal breastfed baby.” As soon as I said I was exclusively breastfeeding she told me I needed to stop and switch to formula since babies only need to breastfeed until 4 months and with her weight loss (from being sick) I needed to put her on a schedule and stop feeding on demand. I wasn’t quite sure how to react so I just nodded my head and accepted the formula samples she handed me. She scheduled another follow-up weight check for Thursday morning, 24 hours from now, and said she expects to see her above 12 pounds by then. What?! Am I crazy for thinking that’s a pretty steep expectation from a sick baby? After the appointment today all my daughter wants to do is nurse, won’t take any formula we were given and is still refusing any kind of baby food. How am I supposed to get her weight up before then if she won’t eat? The ped made my husband and I feel like we weren’t good parents and that we had no clue what we are doing. I’m not sure what will happen if her weight isn’t up but I’m stressing out a lot about it and feel like I’ve failed now. I’m sorry for ranting.