itchy tag-free clothing labels

A few of my shirts have been making my upper back itch lately, even though they are tag-free shirts. Sometimes when this happens and I carefully inspect the shirt, I find a tiny hair or eyelash or some such thing which is the culprit. But the last times, I've found nothing.

I now suspect the tag-free labels themselves are the culprit. The shirts are several years old and the substance (acrylic paint?) used to print the label text on the fabric now has cracked and the edges of the cracks stick out just enough to irritate the skin.