The credit card applications got blocked, but I found out about them because the thieves used my email address on the applications. The most frustrating part was trying to get in contact with the right people at T-Mobile and Verizon to report and shut down the fraudulent accounts. I found out about those because of soft credit pulls on my credit report. I'm not sure if a credit freeze would have prevented them since they were just soft pulls.
Sorry you had to deal with that, sounds like a nightmare.