she probably got sick from the shot as antibiotics can cause them to vomit and a strong dose from a shot is stronger than pill and more long acting. My guess is the antibiotic made her sick to her stomach. Keep an eye on her as some dogs can have an allergic reaction to antibiotics as well. I do not think this is parvo. Parvo is bloody diarhea and yes green goo in eye is an eye infection for sure
info on parvo
Parvovirus: Serious Diarrhea in Puppies & Dogs
sounds like the ER are a bit quick to jump the gun to parvo to me i would say that is a red flag that the er is not the best facililty freaking someone out like that -- crazy
also we had shih tzu too and yorkie sadly have more health issues and poor immune systems as they are inbred so much as they are one of the top 3 breeds
this leads to problems like you are experiencing sadly -- i have a girl yorkie with a poor immune system. Be careful not to over vaccinate and titer when you can after puppy shots. Do not pluck ears as that can cause infections in the ears.