I am sorry to hear about your condition.
Your circumstance is very specific. Most of the knowledge shared on the forum is about indoor pools or spas where UV in addition to chlorine can make sense, or residential outdoor pools where it generally doesn't. But it sounds like you are looking for a chlorine-free outdoor pool. This is an expensive proposition that is not usually recommended here since the chlorine level needed in a residential pool is rarely of any concern. Of course, you have an exception, and your health is worth expense.
In the process of oxidizing organics, chlorine can produce VOCs. In outdoor pools, this is almost never a problem since the release is so very low, and of course they are released into a huge, perfectly ventilated area. Going chlorine-free is not done with UV alone, and it will be expensive. The only question in my mind is whether the VOC level in the outdoor air near your pool is increased in any noticeable way by chlorine doing its job of oxidizing organics. In a well-maintained pool, most of the chlorine loss is UV burn-off from the sun which doesn't create VOCs.
I don't have expertise in this to do anything more than ask questions on whether the level is of significance. If it is, you'll want to look at the expensive options. If it's not, you may want to continue with chlorine and keep your pool well-maintained so that you're never oxidizing large amounts of organics at a time. Perhaps chem geek can provide some level of quantification.
My gut feeling is that the VOCs in the air around your chlorinated pool are several factors lower than the levels you'll find indoors.
