Hello Rebecca,
I agree with Jerry that your family member may be under stress that is manifesting itself in paranoia. You'll not find out unless she speaks with a professional who is in the best position to determine this. Feel her out. Is she willing to talk with a therapist or social worker? Perhaps you could offer to drive her there.
The best way to frame it is to suggest that you're concerned without stating that you believe the family member is sick or has schizophrenia or a mental illness. At this point, you just want to put her mind at ease.
Best,
Chri