You can look at the query cache: http://www.databasejournal.com/features/mysql/article.php/3110171/MySQLs-Query-Cache.htm but it might not give you access to the actual queries and will be very hit-and-miss if it did work (subtle pun intended)
But MySQL Query Browser very likely maintains its own list of queries that it runs, outside of the MySQL engine. You would have to do the same in your app.
Edit: see dan m's comment leading to this: How to show the last queries executed on MySQL? looks sound.