I think doing the credit freeze is probably sufficient (if it works for your situation).
After being informed by two different major companies that my info may have been compromised, I took that route. It's fairly easy, but I offer this one warning: be careful when setting up your account with Experian. I had no problems with the other two, but Experian may be the most inept at online security of any company I've ever dealt with - it's a long story, but be very careful when using their website.