Did the vet offer a reason for the statement regarding the eggs? Is the vet, for example, claiming that she will be on mediation that would render the eggs inedible for humans and, if so, which medication is it and for how long will she be on the medication? In order for the feathers to regrow...
So sorry about your little hen. Can you post a photo of the wound so that we can better see the location and details to offer suggestions on how to best address the picking?