From Podpedia

A braghumble is when someone brags about something to make something embarrassing sound even more embarrassing. The term was coined by Brady. Brady used the example of bragging about having interviewed a famous person to later tell that he had a streak of toothpaste on his face during the interview. Brady explained that bragging about that interview makes the toothpaste even more embarrassing. The term braghumble was named after the term humblebrag.