Do you know which blankets you have? Is it possibly the velvet one with the satin like binding all around?
I have had some pilling on the binding of mine, and it has come from the fact that I use it in conjunction with flannel sheets. The only place I have the pilling is on the binding itself, not the blankets themselves. Q sells a gizmo that is used to shave pilling off sweater and such. I got one for a gift, and love it. A device like that should clean it right up.
I'd also suggest washing each blanket by itself, to avoid one's shedding ending up on another.