I wouldn't be without a press cloth, but you can substitute using a tea towel, like muslin, or a thin towel with most of the nap gone, yes an old pillow case or sheet will work..
A press cloth can be purchased at a fabric store or where they sell sewing items. A press cloth is ideal for use on anything that you don't want to "shine" after ironing. Dress clothes, suits, silks, knits, wool, corduroy, suede or anything that can melt if iron too hot.
Take a trip through JoAnn's, Hobby Lobby, or any fabric store or quilt shop to learn about fabrics, and muslin. Muslin doesn't have lint like some cottons and is used in many things.
Back in the "antique days", flour, sugar and seeds used to come in sacks made out of muslin, which they used to bleach the sacks and use them to make clothing and other things. Some can be almost heavy as canvas and some very thin and light weight. Muslin made great Dish towels, often called "tea" towels. It was absorbant and no lint like terry cloth. Women often made fancy edgings and embroidery for decorations and gave them as gifts, used in picnic baskets and wrapping baked goods, besides using to dry dishes.