Does he perhaps mean "Only she knows how I feel"? That would make sense, meaning "She's the only one who knows how I feel". But as stated the line can't mean anything sensible. It could imply, "The only thing she does is know how I feel" (She doesn't breathe, eat or anything else, besides knowing how he feels, and that would be nonsense). Or else it could mean that knowing is the only thing she does relative to how he feels -- she doesn't feel how he feels, she doesn't like how he feels, she doesn't care how he feels, etc., she only KNOWS how he feels. But that meaning wouldn't go along at all with the song's overall message. So he must mean what could be correctly stated as "Only she knows how I feel."