Do you go out in public? Do you know how many people you must come into close proximity with who have "stomach bugs?" My guess would be quite a few. Do you come home from the grocery store or the mall feeling anxious with an upset stoamch? Probably not.
So this only happens within your family when you KNOW there's a bug on the lose.
Do I have that correct?
If so, I agree, you really do need help. Therapy is pretty much the only thing that will help you identify why you feel like this and help you overcome this phobia. Normally I would advise a medical check up first, but since this only happens to you when a family member is sick, I'd say pass "GO" and head straight for therapy.
Peace
Greenlydia