Are you allergic to wool, or are sensitive to itchy yarn and find it irritates your skin?
First of all, take a note of the weight (DK, Aran, etc) and the recommended tension of the yarn that you are trying to avoid.
Have a look for yarns with similar weights and tensions on our site. You can select the weight and tension, as well as the fibre, using the controls on the left of the screen and you can find more detailed information by clicking on the name of the yarn.
Different fibres behave in different ways and substituting the fibre may make your item look different to the pattern.
Cotton and linen are heavier and have lovely clear stitch definition. Acrylic is easily washable but not as warm as wool and can stretch out of shape over time.
Merino wool is often suitable for sensitive, but not allergic, skin as it has a high twist so the fibres don't prickle. It's lovely and warm, sometimes superwash, and light with good clear stitches, but a little more expensive. Pure wool is hard-wearing and warm and not always as itchy as you might think.