Kate, thank you for all that information you sent. I had suspected that perhaps the health details that Fr Reilly had mentioned were actually symptoms, as your description seems to support.
I did some more research today, and did locate Fr Dan E. Reilly in housing with other priests on Wentworth Av. (?-hard to read the name) in Chicago on the 1910 census. A blog reader also sent me a list of names of assistant pastors from St. Anne's parish in Chicago that nearly matches the names in the census for that household...besides, the census showed their occupation as priest. So that was easy.
What I'm having difficulty with is finding any parish or diocese news of a historical nature that would include any bio for this priest. I have found such records in other archdioceses (such as Columbus, Ohio), but unfortunately I have found nothing so far for the Chicago area...and St. Anne's itself is no longer existent.
If you have any suggestions of resources that would address the bio for parish priests, I would appreciate knowing about it.