He proudly showed off his new car.
You have a smug look on your face.
自慢げ focuses on the boastful attitude itself, while 得々 emphasizes the triumphant, self-pleased manner in which something is said or done.
Standard kanji spelling.
Variant spelling using げ instead of 気.
Compound of 自慢 (じまん, 'boast, pride') and the suffix 気/げ (げ, '-like, seeming').