Sometimes, when I'm in a hurry, I confuse those cases because the 'basic questions' are "z kim? z czym?" for Instrumental and "o kim? o czym?" for Locative. So I must have asked myself "przy kim? przy czym?" and then mistakenly written that it's Instrumental. It is indeed Locative. As it will also be "o stole" (about a table). Fixed my comment, thanks for noticing and sorry for the confusion.
The speaker isn't really present in this sentence. The subject is "my house", and "dom" is masculine, so it has to be "mój dom". The object (?) is "my school", and "szkoła" is feminine, so it would be "moja szkoła" in Nominative, and as "obok" takes Genitive, it's "mojej szkoły".
The gender of the speaker has absolutely nothing to do here. A boy and a girl will say the same thing.