have a swelled head
To be conceited, arrogant, or self-aggrandizing. Cheryl has such a big head on her, all she ever talks about is herself. Janice has had a bit of a big head ever since she got that promotion.
swelled head, have a
Be conceited, as in Winning all those prizes has not given her a swelled head, at least not yet. This idiom began as be swellheaded, first recorded in 1817. The present form dates from about 1860. For a synonym see big head.