How can one get rid of the whispers of hypocrisy and showing off, especially when performing acts of worship away from public view or when one feels that he is being watched?

These are whisperings from Satan to deter you from worship, so do not pay attention to them. Al-Izz ibn Abdus-Salam explained that Satan calls to abandoning acts of obedience. If a servant intends an act of obedience, Satan casts ostentation into their heart. If the servant does not obey him, he deludes them into thinking that abandoning an act of obedience out of fear of ostentation is sincerity, and this is a lie from him. So, cast away these whisperings and proceed with your acts of obedience, keen on sincerity and far from ostentation.