I suffered really badly at first with uncontrollable sneezing from chlorinated water entering the sinuses, it was horrible like having the flu.
I persevered it te chlorinated pool and i seemed to build up a tollerance to it over a few monthd of swimming 3 times a week.
Obviously try not to let water get up there in their first place but it does happen.
There are also different types of chlorine in different pools
My local has proper chlorine and that one is where i got the irritation from, but there is another pool nearby which i swim at on occasion and this pool uses "salt" as a disinfectant it is actuall
Sodium Hypochloride (salt based) this is much easier on the sinuses.
Ask at your local pools what chemical they use and maybe try one that uses sodium hypochloride