So would this be an answer to "Cén chaoi a bhfuil tú?" (I might have that a bit wrong.)
Or would the question be different for the answer to be "Níl caill ar bith orm." ?

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I'm very much a beginner learner. Don't hesitate to correct me, as long as you explain why. This is how I learn best!

Yes you can use it as an answer to "Cén chaoi 'bhfuil tú".

In Ulster too, you can say that:
- Dé mar atá tú?
- Níl caill orm.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne