Funnily enough, those people who think that their pieces of writing (all art really) aren't good enough, are usually the people who's pieces ARE good enough, or soon will be, but they hold themselves to such high standards that they think they aren't good enough.
I used to write songs and shorts quite often, and the thing is, you should really try to get some feedback on it. Ask some friends that are into writing to have a look at your work to get some feedback if you don't want to post it online.
For me, writing on paper is a much safer space. It's also worth a try.
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