Hey, sorry for the slow reply. Generally, no you'll probably be fine with non-stick pans. The precursor chemicals used for making teflon are definitely not good, but once it gets into your pan it's mostly ok. That said, if you get the pan too hot (think no food in it and its just sitting on a hot fire) then I believe the teflon can offgas which is bad for you. Also, you should use bamboo/wood/silicon utensils on non-stick pans. Anything else can scratch it and take off some of the teflon. Once it's been scratched it becomes very easy for bits of teflon to come off in your food and parts of the layers to continue to peel off. If you scratch it you should either see if the manufacturer will replace/fix it or probably toss it. You don't want to be eating the stuff that flakes off the scratched areas. While teflon is I think technically inert (which is why it's used everywhere) I don't think it's healthy to have that passing through your system.

So, if you take good care of your non-stick pans you'll mostly be ok. Basically just baby them and make sure they're in good condition and you should be fine.

Stainless steel doesn't have this problem but of course isn't as non-stick as teflon or the teflon-similar materials out there and can be much more expensive depending on quality levels.

I wouldn't throw them out if I were you, but would invest in some high quality utensils to use with them (silicon on the end and bamboo for the handle part) so you never scratch them. Oh, and of course when cleaning don't use anything metallic like steel wool/mesh on them. Even barkeepers friend has potential to be too abrasive and take off some of the layers. Soap and water when it's still hot is a great way to make cleaning the pots/pans easier.

Hope that helps!