Can I get rid of yarn fuzz in my knitting project?

I bought some Lion Brand 100 percent wool yarn because I love the color and I want to knit a special scarf with it. I'm a new knitter, and I had never used wool or Lion brand yarn before. I'm trying to make a scarf with a pattern on it. The problem is, the yarn is coming out fuzzy as I knit. It's like there's this coating of fuzz all over my scarf and it looks so ugly. It also makes it harder to see the pattern I'm knitting. Is wool yarn normally fuzzy when you knit with it? Can I do anything to get rid of this horrible fuzz? The yarn is "bulky" and it's the alpine wool kind. Did I made a newbie mistake by buying something that looks simply terrible?