Depending on how wool sensitive you are, you might still be able to use some of the wool sock yarns out there. Generally, sock yarns have a tighter twist in the yarn, so they don't even feel "wooly".
I would avoid acrylic yarns for socks, simply because the end product won't breathe, and you really want socks to breathe. But there are lots of nice cotton sock yarns out there, such as Panda Cotton (which is actually a bamboo/cotton blend).
I use Online Cotton Supersocke, it's 45% cotton / 40% wool / 15% nylon. You'd probably have to feel it, but it's extremely breathable and not "wooly" at all. If you need one without any wool at all, I'm sure there are still several options. It's good that yarns have come such a long way! And you'll absolutely never regret spending the time to learn how to make socks - they're my favorite :D
I hope you find a yarn that doesn't bother you. I have trouble with wool too, but find I can tolerate a blend with wool in my socks. Some people take a loop of the yarn they want to test and wear it around their wrist to see if it is bothersome. You could try some around your foot??? There are cotton sock yarns, but I can't think of the names! Good luck! Socks are fun! samm