what kind of thread,size, and needle are you using?
where did the batting come from?
is it the same batting as from the Dream Batt company? or a knock off from somewhere else?
i've used lots of Dream batts and have never had any problems like you describe. is it a cotton batt? maybe you could try some 'thread heaven' (a thread conditioner) or bees wax to help your thread glide through better. or a smaller needle? chances are the (fuzz) will wash away when the quilt is finished & laundered- does the package say it's good for hand quilting? sorry i don't have more (tips) need to know more about the batting i guess.