I think every line in this song is underscored by a desperate need for me to know what to carry, to turn off my very critical eye sometimes, to be fit for the shoes I've been given.
It seems to me that "to carry" in this case may mean "to carry a weight". So I suppose he's saying that in every line he wants/he expresses his desperate need to know what weight he will have to carry in his life, I guess.
As for the shoes, I guess it means that he has to accept the life he was given?
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His critical eye is his own. It represents the sum of his experience and the judgement he's developed along the way. But in order to do justice to someone else's lyric, he needs to play a role.
My guess is that he's referring to the "shoes" which represent the role he assumes in a particular song. They belong to the character he plays.