"Trivia" is used most often in an "uncountable" way, just like "wisdom" and "water". It makes sense to be "filled with" or "full of" any of these things.
"Filled with" would sound better than "full of", but "full of" is correct.
"Triviality" is an equivalent word that is used in a "countable" way. To use it, you would need the plural: "You are filled with trivialities".