If Our Lord ever went to somebody's "school", it wasn't Rabbi Hillel - rather his cousin, St. John the Baptist, whose baptism he received and than whom he said no one greater was born of a woman. Like St. John's, his public ministry began in the wilderness.
He appeared to be self-taught (i.e. not the disciple of any famous rabbi): "The Jews were amazed and asked: How did this man get such learning without having studied?" (John 7:15)
Also, he says: "But you are not to be called rabbi, for you have one teacher, and you are all brothers." (Matthew 23:8 )
This is because of a Messianic promise that he came to fulfill: "It is written in the Prophets, ‘And they will all be taught by God.’ (Is. 54:13; Jer. 31:34) Everyone who has heard and learned from the Father comes to me." (John 6:45)