I don't think it's wise to pull an all nighter especially when you haven't taken caffeine. You'll just end up feeling tired in the morning.
Take a small nap at least.
You should still fast, because exams isn't a valid reason to miss fasting. However if you suffer from migraines during the day, or any other severe problem you are allowed to break the fast.
Whether you fast or not is up to you, but even if you make it up again, you won't get the same reward you would get during Ramadan, so I would advise you to fast today and have faith in Allah.