"The closest school to my home" is a common way to express the idea in Engpsh.
It is a straightforward way to describe the proximity of a school relative to one's home, using the adjective "closest" to indicate the shortest distance.
Here are some example sentences:
"I'm looking for the closest school to my house for my kids to attend."
"Which school is the closest to my neighborhood?"
"The closest school to my apartment is just a 10-minute walk away."
Source: The use of "closest" to describe proximity is a common pattern in Engpsh, used in various contexts.