Fredzia Brzezinska seems like the likeliest choice to have signed the album as "F. Brzezinska" for school #17a. She was born (depending on the document you look at!) in either 1932 or 1933, a little young for school #17a but not outside the realm of possibility and certainly a better match than any other candidates.
There appear to be two entries for her in the Lodz Ghetto Inhabitants list: Fredzia Brzezinski, listed as having been born on December 28, 1933 and living at Hanseatenstrasse 26 and Inselstrasse 17 #5; and Fredzia Brzezinska, listed as having been born on January 1, 1932, and living at Hanseatenstrasse 26 and Inselstrasse 17 #4. The similarities of the names, addresses, and birthdates lead me to believe these records refer to the same person. I wonder if there are other documents that might be able to tell us what's right.
I believe Fredzia's parents are Dwojra Brzezinska and Izaak Brzezinski/ska, born in 1911 and 1906 respectively. Both are also listed with two records: one with Inselstrasse 17 #4, and the other with 17 #5. Maybe they changed apartments? Maybe one of the records is wrong?