If, as you say, the signs usually appeared near medical facilities, it could be for Navy Pier itself. From navypier.com:
When the U.S. enters World War I, the Pier houses several regiments of soldiers, Red Cross and Home Defense units as well as a barracks for recruits.
1918 - 1921
The Pier boasts its own streetcar line, theater, restaurants and an emergency hospital.
Forum: Forgotten Chicago Sightings