What helped me was to write down dot points of what I wanted to say. Keep it simple and personal. Make it about the school and not you (it sounds kinda tacky and almost prideful if you only talk about yourself- maybe briefly mention things that you do around the school community).
Also the staff are just as important if not more so. You want to make sure that you reach them as well. Maybe thank them for how much they have done during the lockdown for us (also give details). Also, stay away from quotes unless they directly influence or matter in the speech. Often people will just chuck in one to sound fancy. You don't need great quotes to show someone that you are a great person!
I cannot stress how important it is that your speech be personal and almost entertaining. If you start to talk about boring things then no one wants to listen. Put in a joke or two and keep the language informal (e.g. no big fancy words- it may make you sound more eloquent but kids could care less). For a joke keep it lighthearted and maybe even a pop culture reference that everyone would know?
I know that I have written a lot and it may seem daunting, but you can do it. Just remember to keep it simple and lighthearted. Make a list of what you would do as school captain (make sure that it sounds exciting), something positive about the students and staff (maybe in relation to Covid), and then some related humour and inspiring words. Once you write what you want to include it all should just come together.
I would recommend if you need some inspiration, watch a lot of high school speeches, especially the American Valedictorian ones. They usually get personal and every word sounds interesting.
(watch how he presents himself and how he talks. Besides his intro, he gets personal and speaks how a normal person would. Obviously you don't have this much time, but you still have enough time to leave a personal, entertaining impact.)
The way you speak and present is SOOO important. If you look shy or nervous people will know. Be confident, positive and passionate! Because you are! The only thing I can recommend to help with this and stage fright, is just PRACTICE. You will feel more confident and less nervous if you know that you have practiced it a lot. Think of it like an exam. If you don't study much, deep down you know that you are going to do bad. Whereas, if you study a lot, then you will feel good and know that whatever mark you get, you still did your best! If you truly believe and are proud of everything you are saying, then you will show it!
And now I am just seeing that this is a lot! Sorry! I hope it helps though. Don't let it get to you, just think of it as a quick speech- I promise that if you write something that comes from the heart, you will feel good about yourself, no matter what position you get.