What is the ruling on reciting and memorizing the Qur'an while experiencing whispers of showing off and sometimes seeking praise?

You must strive to memorize the Qur’an and recite it frequently. Fear of showing off (riya') should not prevent you from doing so. Rather, fear riya' and strive in obedience to Allah, for abandoning worship out of fear of riya' is blameworthy. As for your desire for people's praise and commendation, this is something ingrained in human nature, and it can be blameworthy or praiseworthy. This can be elaborated upon in previous fatwas.