I didn't know what you meant first by bally. Thought it was going to "ballysomeplace". I know the way you mean and I agree it looks awful. I think it would be more to do with the particular fabric you have chosen, as some materials seem prone to this. Have you asked the shop what they would recommend?
I think there are things you can get, I remember them being called "de-fuzzit" years ago, which was a gadget to remove the "bally" effect from jumpers, etc. Would rather be like shaving your couch. Somewhere like JML or places like that would do them, I would think.