I tried on an angora blend sweater at Gap recently. It was incredibly soft to my hands. I was dismayed to find that it was itchy on my skin, though. I thought it was just wool for me but it seems to be every kind of protein fiber. And linen, man, linen is worse than any animal fiber. Even my hair is itchy if it is in a ponytail and keeps brushing my neck (and I have really soft hair). I suspect it is the tiny ends of the fibers and that my skin is able to detect when they touch me and makes it feel prickly/itchy. Since I decided it was time to knit something for myself I find that I haven’t knit a thing in a month . I think I subconsciously know I won’t be able to wear it. But I don’t like working with acrylic yarn. So what is a girl to do? Is there such a thing as high end acrylic that will last as long as a natural fiber and be as wonderful to work with? My price range is in the “slightly above walmart” category and I have been really disappointed with the options at Michael’s. How can I be a fiber snob and not be able to wear the fiber I am snobbish about?!
What do you knit with if natural fibers are itchy?
What about cotton?
Have you ever tried merino wool? It’s baby soft, super fine wool, often used for baby knits. Next time you’re at your yarn shop, take a skein and hold it on your neck, or in the crook of your elbow. That’s how I determine if the yarn is too itchy or not.
Angora can certainly be itchy, especially if it’s made from cut fibers instead of plucked. If they shear the rabbit, the fibers have blunt cut ends which are coarser for obvious reasons. If the rabbit is plucked, (they gently pull the loose fibers out as if you were combing a dog or cat), the fibers have a more tapered end and are softer on the skin. But sheared angora is cheaper than plucked, and is what you’ll often find in commercial angora sweaters. They also aren’t so careful about removing the coarser guard hairs from commercial-use angora. That’s also why some balls of angora are so darn expensive… it’s the goooood soft stuff. 
I recently found a wool-cotton blend yarn at a Jo-Ann’s Fabrics. It was incredibly soft, couldn’t tell it was wool at all. My only question about it was how do you wash it? But it might feel better on your skin than a pure fiber.
Try some microfiber yarns? They’re ultra-soft. Lion Brand Microspun is the first one that comes to mind, but it’s terribly splitty. I’m sure there are others, though. And blends that might not irritate your skin.