Dreams involving severed heads can be quite intense and often represent feelings of detachment or a struggle with one's identity. Holding your own severed head may symbolize a disconnect from your thoughts or emotions, indicating that you might be feeling overwhelmed or confused about a situation in your waking life.

Throwing your head into a pool could suggest a desire to let go of these feelings or to cleanse yourself of certain thoughts or aspects of your identity that no longer serve you. The pool might symbolize emotions and the subconscious, reinforcing the idea of diving into your feelings or confronting them.

Your father's presence and inquiry could represent an authority figure or a part of yourself that seeks understanding or validation. Your indifferent response might indicate a sense of resignation or a coping mechanism to avoid dealing with deeper emotions.

Overall, this dream could be encouraging you to reflect on your current emotional state and consider if there are aspects of your life or self-perception that need addressing. It may be helpful to explore these feelings further in your waking life, perhaps through journaling or talking with someone you trust.