Hi mta113! Welcome to the forum and congrats for your first (very short) lucid dream ! 
As you’re using a “hand + RC” technique, you can perhaps try the looking at your hand technique. It’s very simple and not so different from the technique you’re already using.
Another very simple technique : autosuggestion. When you go to bed, before falling asleep, repeat yourself mentally : “This night, I’ll realize I’m dreaming”. You can repeat this 20 times, or 50 times, or until you fall asleep, do as you please. You can also combine hand technique and autosuggestion, repeating “this night, i’ll find my hands in a dream and realize I’m dreaming”, etc.
About school, I see 2 methodes : the first is doing a reality check when you’re in school IRL, so next time you’ll be dreaming of school, you’ll make a RC and achive lucidity; the second is visualisizing your school before sleeping, and imagine it’s a dream in which you become lucid.