That "chloriney" smell is not chlorine but chloramines (CC). Sounds strange, but whenever you smell that it doesn't mean you have too much chlorine in there but need more. Sounds weird, I know. I'd go ahead and add enough bleach tonight to get back to shock level. (Especially since it rained. Rainy days can add debris and organic matter to the pool.) The more consistently you keep it at shock level, the faster it will get cleaned up.

I agree about the old pool noodles. I find the fuzz in my pool, too.