Blankets are producing a lot of lint after washing

I recently moved to a new apartment, and when I tried washing my blankets for the first time, they came out absolutely covered in clumps of lint. I have now tried washing 2 fleece blankets and both have come out this way. Both were new blankets, so I tried rewashing one over again, as I thought one should do to help with lint from manufacturing, and if anything it has made it worse. This happens even with the blanket washed on its own, on the recommended washer/dryer settings on the tag (cold wash, tumble dry/"delicates" on the dryer in my apartment building). Has anyone seen something like this happen with blankets? How can I efficiently remove the lint and prevent this from happening in the future?