What you are smelling are probably chloramines, a by-product of
chlorine reacting with debris in the water, which become fumes.
Generally, these chemicals are caustic to asthmatics and others with
respiratory problems.  

The best thing to do is talk with the staff at the pool facility and
make sure that several things are happening which will ensure a
reduced toxic breathing environment:

1.  Are they replacing water in the pool daily?  5 gallons per person
per day is a good rule of thumb.  In other words, if 100 people use
the pool each day, then they should be pumping out 500 gallons of
"used" water and replacing with 500 gallons of fresh water.

2.  Are the swimmers taking a soapy shower before entering the pool
area?  Washing off oils, hair products, dirt, etc. will result in less
caustic breathing fumage.

3.  Is the air being circulated correctly?  Is there proper venting
and fresh air coming into the building?   You'd be surprised at how
many facilities don't stay on top of this.

4.  Do a lot of children and/or elderly people use the pool?  If so,
then there will typically be more urine in the pool, hence a higher
chloramine concentration in the air, and a higher maintenance effort
is required to meet safety standards.

I wouldn't count on it.  Opt for and insist on cleaner air instead.