an inordinately grand opinion of oneself; conceit.
Origin of swelled head
First recorded in 1890–95
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019
swell-headed or swollen-headed
informal an inflated view of one's own worth, often caused by sudden success
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012