Sweater for Mom

I have been working on this shrug from Lion Brand called Barcelona (free PDF pattern) for my mom. It's been about a month now and it's looking alright. The only sections remaining to knit are the edges on the back piece and the front, which also includes the collar. It's probably not going to look as nice as the one in this picture. I am also uncertain as to how it will fit my mom. She is however, very appreciative of the gift. I think it's because my interest in knitting reflects her own and we can bond with this common interest. Although it is a shame that she has no time for knitting now.

My piece uses the exact colour of Homespun as the pattern indicates. The yarn is very soft, economical and quick to knit up but it does fuzz a lot, even when I am not constantly unravelling and reknitting to fix my mistakes. I wonder if there is a way to defuzz or stop premature fuzzing. Should I be wearing gloves to keep from sweating on the yarn when I work too excitedly?