After the promotion, he became so swell-headed that colleagues avoided talking to him.

swell 本义是"膨胀、肿胀"，引申为"骄傲自大"的意思。 headed 是 head 的形容词形式，head 本义是"头部"，这里指"头脑、思想"。 swell-headed 是形容词，字面意思是"头脑膨胀的"，比喻"骄傲自大的、目中无人的"。