After much floundering around with the information_schema.tables table, I finally discovered the answer to your problem - update time doesn't work for InnoDB. See the points here by a.out and ajacian81.
The only way you can do this is to implement logging tables (as suggested by Bill Karwin, a bit of a MySQL/database guru).
The only other thing that I can think of is to use a backup and use a diff programme to compare the text output of queries from your current and backup database. Horrible I know, but there are tools which can do this if it's critical. There's MySQL's own (MySQLdiff - in utilities), you could try Liquibase or Flyaway (which I believe have this functionality) or Google "database diff programmes mysql".
I also found this post helpful in realising that the information_schema tables are dynamic.
Maybe I'm a bit OCD too (can't let this go! :-) ) but I also found this thread - check out the answer by Jacket - Percona may be the way to go if you are in real need of this functionality. However, it's obviously too late for your particular situation. I think it's backups for you :-(.