There is a such thing as chlorine poisoning. If you inhale or ingest too much chlorine it can cause these symptoms. It is possible that the pool is using too much chlorine due to all of the people in the pool. You might want to avoid that pool and try to find another who doesnt use as much chlorine. Some pools now use Bacquicil that has no smell and will not irritate your skin or anything else, it is very easy on the body. You can also find pools who use no chemicals at all, just random household items that work just as well and should have little or no effect on you. If you are concerned, you should see your doctor to check the chlorine levels in your body. If they are high, I would submit those results to the owner of the pool and let him/her know that if you are getting sick there are probably many more who are getting sick as well, and maybe it will convince them to start using the proper amount of chlorine. I hope this helps. Good luck and I hope things get better soon.
Yes its possible that you could be allergic to chlorine. The only way to tell for sure tho is to see a doctor and have them run tests. It could also be just that your swallowing the water and chlorine just isn't meant to be ingested. a little is fine, but you should watch out for how much you getting in your nose and mouth. Also, is the pool heated? I find that if I'm in a warm pool too long (yes a half hour is still a long time in this case) that i feel sick after. i would definitely speak with a doctor tho.
Perhaps, if it's a public swimming pool, it might be an infecton from E. coli It is a bacteria, which could be present in public pools. And if you had swallowed the pool water, then there is a possibility of infection.