Song lyrics are often metaphorical, and sometimes stretch the meanings of things to fit the rhyme and rhythm of the song, even at the expense of clarity. In this case, the singer is lamenting their inability to put their feelings into words. Taken completely literally, it's a bit of a nonsense, but we may interpret it as referring to the English language as a whole, rather than to any individual "words." In that interpretation, the singer means that English lacks the ability to express the depth and strength of their feelings, and is "getting in my way" because of this deficiency.
"Words never show up" is grammatical, but it does not ascribe any agency to the singer, which is emotionally unsatisfying. The singer is trying to express a sense of struggling with the written word, rather than a detached feeling of writer's block.
If you're willing to kill the rhythm and just write the whole thing out in prose, it might go like this:
...but I haven't written a single paragraph, because there aren't any words which express how I feel about you.
But nobody would sing that.