Synonyms for Braggart (same or very similar meaning)
WordNet sense 1 (a very boastful and talkative person):
blowhard, boaster, bragger, line-shooter, vaunterWordNet sense 2 (exhibiting self-importance):
big, boastful, self-aggrandizing, bragging, braggy, cock-a-hoop, crowing, self-aggrandisingWordNet sense 3 (feeling self-respect or pleasure in something by which you measure your self-worth; or being a reason for pride):
proudFrom the ODE community, based on WordNetadd/edit