Pills in woolen clothes or "peeling" in English is completely normal. It is usually given more in natural fibers and they are produced by rubbing. That's why jumpers tend to have more pilling in the armpits and on the inside of the sleeves.
The best way to deal with pilling on woolen garments is to have a wooden brush or lint remover and use it from time to time to remove pilling from the garment. It will be like new.
In Lanas Llamas you can find both the charger and the ball-removing machine, both from Prym.
