Did you ask the pharmacist if you could put the medicine IN eggs or did you ask if you could cook them in eggs?
I can't imagine cooking the meds in the eggs. A lot of heat could change the drug.
It's a child's "job" to give us a hard time taking medicine. You give it to them anyway, no matter whether they like it or not. Get one of those long tube spoons that they sell at the pharmacy. Lay her down with a towel underneath her head on the floor, and straddle her face with your knees so that she can't turn her head. Pour the medicine in her mouth as you hold her cheeks so that her mouth is open.
I know that sounds mean, but your child has to learn that she has to take medicine even if she doesn't like it. And it's better than her ending up in the ER having to have an IV put in her vein. She'll like that a LOT less.