If my iPhone doesn't have cydia and I can use any sim, that means my phone is officially factory unlock?

That is an easy test, if the iPhone has not been jailbroken and will accept sims from more than one carrier, it must be unlocked. A locked iPhone will not do that.

Did you buy the iPhone from Apple or another source? If you go to Settings > General > About does it show only info on the sim you are using, the network and carrier? What model is the iPhone? You can also check with Apple and see if the Serial Number is for a factory unlocked iPhone, customer service for Apple is at http://support.apple.com/kb/HE57 world-wide.