'School supplies' is indeed correct, sorry I didn't think of it.
However, to my ears it's used more in the context of shopping, at the beginning of the school year, than in the context of remembering to bring things home or take them to school. And it includes things like pencils, pens, paper, glue, scissors, ruler, compass (if kids even still use all those).
I don't know if we would say 'stuff' or 'things' as much for a particular subject like English. Sometimes we might just use a more specific noun. 'Oh, no, I forgot to bring home my English book / notebook / folder. I'll have to get the assignment from someone else.'