It's hilarious to read about people giving vitamins, various pills, taking the dog to the vet every other day, etc. Wtf? It's a dog, he'll be fine. Water, feed, exercise repeat.
Is it true vomit or regurgitation? Does she gobbler /gulp? - meaning does she swallow big pieces without chewing? Our EM still does this occasionally and then up it comes. Yes he does re-eat it. From reading back thread regurgitation is normal for some dogs when starting raw. Grosses my husband up to no end but the 2nd time he does chew it. We've gotten into the habit of holding his food while he eats it to make sure he takes the time to chew.
Hang in there - she'll get the hang of it.
The antibiotics are more than likely the cause of her diarrhea. All of our dogs have that reaction to them. Poor girl has been through so much and is SO lucky to have you as her new champion!
Look up the recipe for Satin balls in past threads - those might really help her gain some weight back and the small size shouldn't be an issue for regurgitation.