Can you access the account via a computer or web browser rather than the Facebook app? If you have the same problem there that would definitely indicate that the problem was at the Facebook server end, and if not it might let you unlock your account.
(I've never met this security check, so am just guessing here).
The other option would be to email FB to let them know that you have this problem. "We're working on getting it fixed as soon as we can" sounds like a problem at their end rather than on your phone, though misleading error messages would not be unknown (anywhere, not specifically with Facebook).