I'm on the birth control pills (Yasmin), but if the condom breaks, should I be concerned about this?

As long as you have been taking your pills everyday as prescribed you shouldn't get pregnant, although there is that 1 percent chance. The thing you should worry about, if the condom breaks is getting a ually transmitted diseases. If both of you have been tested for VD's and everything came back fine, then you have nothing else to worry about! glad to hear that you are practicing safe :)