The answer is yes. You could be allergic to just about anything in the pool, including substances placed in the water to purify it or to substances that choose to grow in the pool, such as molds and fungi. This is even more of a problem in hot tubs.
This could also be a non-allergic problem. An irritant problem, as can be the case when chlorine levels are too high.
The distribution is peculiar, limited to arms and legs. Any allergic problem would almost certainly be on your trunk, as well. Another possibility is that you are being bitten by mosquitoes or other "wildlife" that frequents the pool.
Whatever this is, it is common that only one person in a group will be bothered. Allergies vary greatly from person to person and it is well known, for example, that some individuals are especially prone to mosquito bites.
Try showering with soap and water as soon as you emerge from the pool. Whatever the cause that might remedy the problem.
sound like you had sex with the wrong person fag