Well, dyeing silk with fiber reactive dyes does mute the shine a bit. If for the next time you dye silk you want to preserve the shine, either use acid dyes or use the procion as an acid dye, with vinegar instead of washing soda, and heat it until it exhausts.
It fuzzed up because the yarn you used seems to be a very loosely spun singles (one ply) yarn. It's probably going to stay fluffy.
Unless you were to knit really tightly with it, it would have most likely fuzzed up and eventually lost some of its shine anyway, since that's what loosely spun silk does after some wearing and washing.