Is my striving to memorize the Qur'an and acquire knowledge generally, motivated by competition and envy (ghibtah), considered a form of showing off (riya') that deprives me of reward, and how can I achieve sincerity in my intention?

The path to sincerity is through seeking Allah's help, being aware of the danger of showing off (riya'), and striving against one's self. Your intention behind any action must be for the sake of Allah Almighty, and you should not abandon seeking knowledge or performing good deeds for fear of showing off. Among the means to achieve sincerity are: striving against one's self, being aware of the danger of showing off as it is a form of shirk (polytheism) that nullifies deeds, and reciting the narrated supplication: "O Allah, we seek refuge in You from associating anything with You knowingly, and we seek Your forgiveness for what we do not know."