1st of all, if you have the Flu today, it is NOT a good idea to do your fitness test tomorrow. You can't be ready that fast.
Anyway, here's what I would suggest. Start out at a pace where you can complete the entire 12 minutes without walking. 12 minutes is a long way for someone overweight so don't go out fast the first lap, die and walk the rest of the way. Start out at a jog, a pace that you can handle. Take it seriously, don't look around at anyone else, watch the track and don't forget......go at a pace you can handle. With 1 to 2 minutes to go (or a distance from which you know you can get to the finish line. I want you to start with a faster jog and finish gutting it out (as fast as possible.) Now this is tricky. You don't want to come across as a person that took it easy and sprinted at the end. I want you to run fast enough to be completely spent at the finish line. You'll get sympathy that way. If a person gives it 110% you'll be amazed at the response. It isn't the individual's size and speed that counts, it is the individual effort that people look at. (If you feel you can't keep the pace along the say, slow down a bit but try not to do a slow walk. But hey, if a walk is the best you can do then walk as fast as you can. put in the effort)