If medical-seeming placebos work, then she will grow up believing that if you are too anxious to sleep, you should take a sleeping pill to cure the insomnia. However, the anxiety will still be there. It is far better to get rid of the anxiety that is causing the sleeplessness.
Better to detach in her mind the "sickness" that is illness from the "sickness" that is nausea, and/or to explain that worrying makes your stomach worry too, and squeeze your food up, so if she gets rid of the worry, her stomach won't be so worried and she won't feel sick (sick as in nauseous) Keep it at a level she can understand and accept, of course, and don't give her more to get anxious about!
Then give her some NON-medical remedy to make her feel that she is in charge of her feelings (and her body's reactions) - perhaps deep breathing, the kind that involves the stomach muscles and counteracts the knotted sensation brought on by fear.
Ae there any simple yoga exercises that would help?