What happens during the swimming unit at school if you get your period, & you don't wear tampons?

You may get stains. If you wear a pad instead of a tampon, water will be soaked up into your pad and it won't be able to absorb the blood that is coming out so you may get blood on your swimsuit. However, not much blood usually comes out when you're swimming. If you do get blood on your swimsuit, it will come out if you rinse it right away with cold water.
Not to Worry. Pressure of water on the outside of the vaginal opening prevents any leaking while you are in the water. Only time you will worry is coming out of the water when your menses may flow like a regular period.