You're not being petty. You got the highest mark and therefore you have won the prize, but instead of giving it to you they're giving it to 'she who yells the loudest'. And why do you say she's smarter than you? You beat her! It doesn't matter what the award is, the point is that you're being screwed for working hard instead of throwing a tantrum. The teacher sounds rubbish. I would write a letter to the headmaster, something like:
"Dear [],
In relation to the award for highest marks in Modern Studies, I was rather surprised to hear that this year, instead of the award going to the student with the highest marks (as has traditionally been the case), the award has instead been allocated to the student with the 6th best marks, apparently on the basis that it was promised to her a year ago.
Without wishing to sound petty, I would be extremely grateful if you could kindly clarify the basis on which the award is issued. You will appreciate that it is rather demoralising for myself and the other students in the top five of the subject to find that they have erred in focusing on the academic side of things. If it is the case that each year the award is given to the student who asked for it most loudly in the preceding year, then please consider this my formal application for next year's award.
I look forward to your views.
Kindest regards, Babybombo."