Synonyms for Braggy (same or very similar meaning)
WordNet sense 1 (exhibiting self-importance):
big, boastful, braggart, self-aggrandizing, bragging, cock-a-hoop, crowing, self-aggrandisingWordNet sense 2 (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