If you created the account on the same day of the fake birth date, you might be able to figure it out (except for the year) by going into your log (under "COMMUNITY >", below GTLIFE and PROFILE).
Go all the way down the log, it will say "New game started" and the date will be on the right-hand side. If you account has seen a lot of activity, though, the log might not go back far enough.