Dreams about school often symbolize personal growth, learning, or unresolved issues from the past. In your dream, being chased by your brother's classmate might represent feelings of anxiety or conflict in your waking life that you feel are unjustified. The aggression from this classmate could symbolize a situation or person in your life that you perceive as a threat or challenge.

Falling down the stairs can signify a loss of control or a setback in some area of your life. The minor injuries you sustained could suggest that while the situation may be challenging, it is manageable and not as damaging as it initially appears. The bus ride home at the end of the day may represent a return to comfort or safety after experiencing stress or conflict.

Overall, this dream might reflect feelings of being overwhelmed or targeted in some aspect of your life, but it also suggests that you have support and are capable of navigating these challenges. Consider reflecting on any current stressors or interpersonal conflicts that may be influencing your emotions. It might be helpful to address these feelings openly or seek support from those around you.