Unless you are a fetus or very young child, you probably don’t need to worry about BPA. Your old Nalgene water bottle - or for that matter, the extremely wide variety of canned, jarred, and otherwise-packaged foods you may consume - is not going to cause cancer.
Freezing things in plastic containers is not going to cause dioxins to leech into your food. This is because there are no dioxins in plastic. Also, lowering the temperature by and large slows down chemical reactions, as opposed to speeding them up, so if you want to irrationally worry about non-existent things creeping from your plastic containers into your food, worry about it happening when things are heating up.
But you shouldn’t worry about that, because if a container or plastic wrap says it’s microwave safe, it’s pretty much safe. Some plastic products that aren’t microwave safe may or may not leech harmful chemicals if they’re in direct contact with your food while cooking in a microwave. The research is still unclear as to A) what happens and B) what the long-term effects to a human are.
So there’s really no reason to worry about heating up that leftover chili. If you do, however, decide to ignore things like ‘scientific research’ and instead pay attention to the alarmist headline written by a journalism school dropout on the cover of your glossy fashion magazine, please shut the fuck up about it.