Now, a mayor is blowing upgoing viral / making the news because he bit a gold medal without getting permission from athe softball player who won it.

I think "going viral" or "making the news" fits what you meant for "blowing up" :) Also, I added more context for the softball player.

First of all, it's out of thea problem to bite other's' property, and it's against the infection control underguidelines in this situation.

He apologized, but he is criticizing again because thebacktracking. His excuse wasis, "iIt was my display of affection", and his attitude wais dishonest.

"Backtracking" is a good word to use here! If someone does one thing but then turns around and does the opposite (like apologizing and then making excuses), that is "backtracking".