I don't write songs, but I do compose tunes. Before I started playing my own tunes, I tried to establish myself as a competent player of traditional tunes. I then started to slip one or two of my own in and I have been quite pleased with response. Quite a few people seemed to like the tunes I wrote, which encouraged me to keep going.

I still take the approach of mixing a few of my own tunes with mainly traditional material (using the term fairly loosely as a fair proportion of what I play has been written by people who are still alive or only fairly recently dead).

I reckon as you gain confidence and, if people like your material, you can gradually increase the proportion of your own material.

My 2p worth FWIW.