If your girlfriend is supposed to have her period today and you used a condom but it fell off but you did not cume should you be worried?

The fact that you didn't ejaculate doesn't mean you couldn't get her pregnant so yes, it's possible she's pregnant but one missed period isn't conclusive, let alone a single day late. A pregnancy test can determine this. You should be aware that condoms are available in different sizes so you should be sure to use one that will not slip off and follow the directions on the box for the condoms and the pregnancy test.