I was talking about putting a freeze on your credit with the credit reporting agencies, not cancelling cards with your credit card company (though obviously that had to be done too). The reporting agencies are EquiFax, TransUnion, and Experian.
If someone has your driving license and other info in your wallet, it's likely they have enough to open new credit accounts under your name unless you put a freeze in place - and eventually the folks who think you owe them money will find you. While the mess can be cleaned up, doing so is as much a pain in the patookus as getting rid of mites.