I looked for it, but it wasn't at school or at home.
I searched for it everywhere, but it wasn't at school or at home.
neither ... nor ... を使って「どっちにもなかった」と言えますが、次のように言った方が自然です。
ーI looked for it, but it wasn't at school or at home.
「探したけど学校にも家にもなかった」
to look for で「…を探す」
ーI searched for it everywhere, but it wasn't at school or at home.
「あちこち探したけど、学校にも家にもなかった」
to search for で「…を探す」
ご参考まで！
カナダ 
