Puppy Chewing Fabric

My boyfriend and I just adopted a five-month-old mutt named Rollie...the shelter we got him from thinks he's part Pomeranian, but I think he looks more like a Jack Russell Terrier. Everything was going really well...he picked up on housebreaking super fast, and we're gradually starting to work on some basic obedience training...but over the last day or two, he's started to chew on fabric. Towels, our sofa, our carpet (and he took out quite a chunk!), even clothes that we're wearing. He shows no interest in chewing on shoes (which is what I would have expected), and we have plenty of toys for him to pick from. When we catch him chewing, we tell him no, stop him and give him something else to chew on, like a toy or a rawhide. But soon after, he goes right back to what he was doing before.

This is my first puppy, so I'm pretty clueless. Has anyone else had this problem? What can I do to deter him? Any input would be greatly appreciated. Someone on another thread said to put stuff he shouldn't chew out of his reach--which makes sense, except I can't do much about the carpet! We do watch him pretty closely when he is out of his crate, but if I can stop the behavior altogether, that would be ideal. Thanks!!