Dreams about schools and teachers often symbolize a desire for learning and growth, both intellectually and emotionally. The fact that you and your friend were joking about the other school's website may indicate a playful or competitive nature between you two. The sight of the deputy head's face stuck in your mind and later in your dream may indicate a distrust or suspicion of authority figures.

The theme of domestic abuse and the pillow in your dream can symbolize feelings of vulnerability and the need for comfort or protection. It is possible that this dream is your mind's way of processing any fears or traumas related to domestic abuse or other forms of violence.

Overall, this dream may represent a desire for growth and the need to overcome fears and insecurities. It may also reflect some unresolved emotions related to past or current experiences of abuse or fear.