'Patches' as they're referred to (basically any logos or pictures ironed or stitched onto any type of fabric), can eventually come off, sure. But you only bought the shirt today and already the patch is coming off? Trust me, you need to return it, like Ashley said, it sounds like a pretty cr*ppy made shirt. If you dont want to take the shirt back or you feel you cant, yes, try an iron on it, but look it up first, you dont wanna go burning the picture! Hope this helps :)
Try ironing it on again if its been ironed on, I would give it a try, then if it doesnt work, take it back
perhaps return the shirt? sounds like it's low quality