Does a young man's abstention from prayer throughout the holiday, due to the absence of a shower in his grandmother's house and his shyness about informing his father of a wet dream, render him not sinful?

It is not permissible to abandon ghusl (definition) (ritual bath) after sexual defilement (janabah (definition)) under the pretext of shyness. What is obligatory is to seek water and perform ghusl, no matter the condition of the bathroom, as long as it conceals the body. Now, you must repent and seek forgiveness, and repeat the prayers that were performed while in a state of janabah, because Allah Almighty says: "O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying or while in a state of janabah, except those passing through [a prayer area], until you have washed [your whole body]." (Quran 4:43)