ANDY'S ANSWER: Although periods are inconvenient, if you allow them to interfer with your normal life, you could end up missing out on a lot of things. This isn't something that only happens once or twice. It happens every month and lasts for up to a week for good portion of your life. You will need to figure out how to work with it, and not just for PE.
If your flow is particularly heavy, make sure you are wearing a pad that is extra absorbant, and change it just before you go to PE. That way even with exercise you shouldn't have any issues. You could also look into wearing a tampon, particularly if you want to go swimming.
If you are prong to period cramping, you might find that taking a pain reliever BEFORE the pain gets so bad that you feel awful is the best thing to do. If you take a pain reliever early, your cramps will not ever get as bad as if you leave it until it gets unbearable.
Your period should never keep you from doing normal things.