Ok, it seems that there is something wrong with your eyes. I think the possible reasons are as follows. In the first place, your eyes are very sensitive to some chemicals and swimming pool contains a lot of chemicals which would be harmful to your eyes. Secondly, you might have got a lot of water into your eyes, and your eyes would naturally feel uncomfortable, that is natural. As to infection, the possibility could be high, because pool water could not be replaced on a regular basis. I suggest that you try to get a pair of swimming goggles to deal with this problem.
It is a common problem among swimmers. The water in the pool is full of disinfectant fluid, which will hurt your eyes if you touch the water for a long time, and that is why we would better wear swimming goggles in the pool. Of course, there can be bacteria left in the pool that may cause infection and that is why we have to wash our body after swimming. However, most of people ignore the eyes. You would better have some eye drops that functions in antiphlogosis now. And for further advice, you can choose a proper set of swimming goggles to swim with next time.
I have experienced it three months ago. Then I searched the internet and found that the best answer was to take a couple of drops of milk into my burning eyes. As we all know, chlorine in the pool helps to break the bacteria down so they can't grow in the water. However, it also changes the pH of the water. The normal range of our eyes ph is slightly acidic (6.8 - 6.9). As time goes by, the PH of the water will dramatically changes to even a high level of 7.8. There is no doubt that our eyes will be hurt. That is why people use swimming goggles, not just for cool. Furthermore, the pH of milk is 6.7, so it can actually works. As a result, although it seemed strange, as I had bottle milk at hand at that time, I tried. Surprisingly, I relieved and eventually my eyes returned to normal. On safe side, if it not get better after your endeavor, you just need to see an eye specialist immediately.
Well, yes, I have to say that you may get burning eyes because of the eye infection occurring in your eyes, when you have swimming. Generally speaking, there are many objects in the pool or sea water which can cause the irritation of your eyes, and eye infection. Anyway, we can say that swimming water can be irritants, so that you may suffer eye infection because of swimming in the pool. And then, your eyes will be burning. Also, in some cases, red eyes, watery eyes, itchy eyes can be possible too. And it can be kind of normal for some people. In my opinion, you can flush your eyes with cool and fresh water after your swim. In that way, it can just relieve it. Besides, saline eye drops are also a simple fix making them an essential swimming item for this summer season.