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.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.