самовлюблённый человек означает в английский

egotist [egotists]▼(person who talks excessively of his or her self)
noun
[UK: ˈe.ɡə.tɪst] [US: ˈiː.ɡə.ˌtɪst]

narcissist [narcissists]▼(person full of egoism)
noun
[UK: nɑː.ˈsɪ.sɪst] [US: nɑː.ˈsɪ.sɪst]