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Adjective: swellheaded  'swel,he-did
Usage: N. Amer, informal
  1. Characteristic of false pride; having an exaggerated sense of self-importance
    "a swellheaded fool";
    - conceited, egotistic, egotistical, self-conceited, swollen, swollen-headed, vain, proud, puffed-up [informal]

See also: proud