Well, it is normal to have burning eyes because of chlorine. And your eyes will feel discomfort, and in some cases, bloodshot eyes, and red eyes can be possible. So you need to take some measures as soon as possible. For example, cold compresses can be tried. And that can be effective to relieve your situation. Also, you can use eye drops, which are a very good idea. Also, you can use a thorough rinsing with cold water, so that it will not irritate the eyes. By the way, at this period, I would suggest that you should not sleep with the contacts, because it will damage your eyes and make the eyes infected.