Thanks for getting in touch. I know there are other Rust families in Illinois. Mine doesn't seem to be associated with those who have or had been in the state for a fairly long time.
If you speak to your grandmother in the near future, maybe she could give you an idea of how her line proceeds, down to her. My great grandfather, James, was born in IL, but left while still young for CA. His parents were born in New York, and probably died in IL. His father's initials may have been D.R. (Rust).