If you smell chlorine, yes. Except that really isn't chlorine, that's chloramines. It's a well-known irritant.
Believe it or not, that strong "chlorine smell" is caused by too little chlorine. Chlorine is an oxidizer. Think of it as flameless combustion. Chloramines are like the smoke from a smoldering fire. Get a good hot fire going and there's very little smoke. Get enough chlorine in the water and it's like a hot fire. The chloramines are the partially oxidized sweat and dead skin and everything else you don't want to think about that's in the water.