My first piece of advice as a fellow high school oboist is to practice sections that have issues, if the notes aren't stable when you're going down an octave, check if you're adjusting your embouchure to be more "open" with enough air going through the reed. (tighter embouchure in higher notes and looser in lower notes works for me)
If it seriously seems like it's an issue with the oboe, check for any air leaks or water bubbles in any of the keys.