Lining a shawl is not a good idea, particularly with the fabric you have chosen, the fabric will shrink and the yarn will not. It would be better to alter the fibre of the shawl to make it useable, soak the shawl in lukewarm water with a bottle of cheap hair conditioner dissolved in it. Doing this will serve multiple purposes, it will block out the shawl, it will help eliminate the uncomfortable issue with the yarn you used to make it and it will eliminate the need for a liner. If you don’t like the idea of using hair conditioner, a generous amount of liquid fabric softener will work as well, just keep in mind that it you use fabric softener instead of the hair conditioner, you will probably have to repeat it in the future after washing it a few times, the residue of fabric softener will be lost but the paraffin affect of the hair conditioner is not lost as easily. Great job on the shawl, by the way!