You are not likely to be able to use a library's or other business/organization's printer to print onto fabric as they'll be concerned about damage to their machines. (not likely to happen, but still.....) You'll have to find a friend who'll let you use their inkjet printer to transfer what you want to print onto fabric.
1. Cut a piece of freezer paper the size of the paper that fits the printer. (This is merely your stabilizer for the fabric.
2. Press the shiny side of the freezer paper, without steam, to the WRONG side of the fabric you wish to use as the label.
3. Trim the fabric to the size of the freezer paper if you didn't before.
4. Line the fabric-fused paper up into the printer so that the printing will be on the fabric -- NOT the paper -- and print as usual.
5. Gently remove the freezer paper from your fabric.
6. Be sure the ink is thoroughly dried before getting this fabric damp or wet. If you press to turn the edges for appliqueing it down to the back of the quilt, be sure to use NO steam. Using an HP printer and HP inks, I have washed many quilts with these printer done labels with no problems, especially after waiting for a few weeks. Even those done in color or with fancy printed borders.
Jan in VA