This isn’t necessarily a low FODMAP post as much as a new to cooking post. If you have an old non-stick frying pan you should consider throwing it out. The teflon that is used contains a chemical that basically can cause various cancers. Any quick google of “why is non stick cookware dangerous” will help you understand why I am suggesting it’s time to throw them out.
So if you are throwing them out what should you replace it with? Well ceramic non-stick are good, they don’t have a long life of non-stick and slowly get worse over time. A more attractive alternative might be to use either a Cast Iron or a Carbon Steel Pan. Both have great thermal properties(They evenly distribute heat), but Carbon Steel is a little more nimble with temperature adjustments. It heats up faster and will respond faster to changes from your range/oven than traditional cast iron. And an added bonus is both of these pans can be thrown in the oven if a recipe calls for it. Something you definitely can’t do with a “non-stick” pan.
I recently purchased two and threw out my non stick. I have to say that there is some work to be done to season them properly. But once you have done that they cook beautifully. I definitely would suggest them as a part of your kitchen tooling.