"Memories of Mundelein", put together for the 75th aniversary of Mundelein, in about 1984, reports the following on Amelia Holcomb:
She was teacher and principal in Chicago. Upon return to Mundelein in 1886 she established a school the Rockefeller Classical Institute. She also organized a Sunday School.
There is no mention that she started a second (non religious) school. Also, there is no mention of music in the two paragraphs concerning Amelia Holcomb. This indicates her one and only non religious school was most probably an academic school.