What kind of rash? Where? Is it in an area where there is rubbing/chaffing? You can try Body Glide or some other lube.

Most public pools put WAY too many chemicals in the pool. Good to keept he creepy crawlys down, but bad for your skin/eyes/suit.

I have to slather myself in moisturizer after swimming to keep my skin from drying up and falling off.

Yes, different people have different reactions to chlorine and to bromine. Find out which one is used at your pool. If possible, switch to a pool that has the other stuff. I have trouble (extreme itchiness) with bromine but chlorine is fine for me. Also, you may find that as your skin becomes used to your increased frequency in the pool the rash may diminish.