#Fear of disease (or illness) is known as nosemaphobia or nosophobia.— The Encyclopedia of Phobias, Fears, and Anxieties, Third Edition
As you have said, this isn't just about your daughter's sickness phobia, it is also about her fear of being separated from you.
My 20-year-old daughter has a phobia of being sick
Baimė, kad gali susirgti arba sergi kokia nors liga, vadinama nozofobija
Nosofobija gali išsivystyti ir tarp kibernetinių hipochondrikų. Ji gali padidinti nerimą ir paniką, patiriamą galvojant, kad galima netikėtai susirgti.
4. HUMAN HEALTH and PHYSIOLOGY