Cold War is not WWIII and that sort of navel gazing self mythologizing simply detracts.
The dispute between the U.S. and Iran dates way back to 1953, when the Eisenhower administration supported a British effort to topple the duly-elected government of Mohammed Mossadegh and install the Shah as the head of state.
Gazing? Over 5 million people died in the cold war! Damn right it was WWIII! Fought Koreans, Vietmanese, Chinese and Russians! This is WWIV!
The title really doesn't matter, but the people who were kept in Teheran for 444 days (1979) or the 243 Marines who died in Beirut in 1983 -- both acts by Iran -- would probably not agree with your 9/11 date. This war started a long time ago; most of us just didn't realize it until 9/11. Hell, some Americans and most Europeans don't realize it yet.