Don't worried, it will be ok the next morning. You can rinse your eyes with water gently. Tears can also help you to get rid of the burning eyes, so try your best to cry out and shed off the tears, then you will feel better. You can make use of eye drops, too. Burning eyes are temporary and do not last long, wish you better soon.
If your eyes get burning because of chlorine, you could use the warm compress to make your eyes feel comfortable by finding the hot water and clean cloth. You could also use some eye drops before you sleep to get rid of the invisible bacterium in the eyes. You could also drink more milk to make yourself feel comfortable.
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.