You get to pick the ingredients but what are the limitations? Why only a frypan and a couple of saucepans?
Does it have to be a dinner entree? Is there a theme to the competition? What ingredients have you chosen?
Some more information would help.
You are a breakfast cook so cook some breakfast. There are so many things you can do with eggs.
Remember this is all for fun so relax and just have a good time.
You can, of course, choose dinner items in keeping with what everyone else is doing.
But I would suggest sticking with your strengths. Start thinking of variations on eggs.
You can do a bed of julienned vegetables, two poached eggs and a sauce on top.
Or a bed of hash made with whatever protein is available, with two eggs and a sauce or garnish.
Or a warm salad with bacon pieces and two soft poached eggs.
Shirred, poached, en cocotte, scrambled, hollandaise.
Steak and eggs, salmon and eggs.
A fast stir fry of whatever is available.
Much depends on what ingredients you will have available so if you will not know the ingredients in advance,
start thinking about what kind of dishes you can make in twenty minutes. Obviously any dish with long cooking times isn't going to work.
In any case, your work habits will be most important. Stay focused and concentrate on working clean and neat.
Twenty minutes will mean short cooking times for the food because much of your time will be spent chopping, organizing your work, etc.
So when faced with whatever food is available, think of how to get it into smaller pieces quickly so you can cook it in just a few minutes.
If you can find out what the food is in advance, that will help guide your thinking so when you get there you are more mentally ready.