I don't have dry skin or hair, I'm pretty much oily, but I have heard the benefits of using a silk pillow case for a long time. I decided to try it out about six months ago, and I'm so happy I did! The silk pillow case feels amazing against your skin, it's cool and soft. I also stopped waking up with crease lines on my face, which I would get from cotton pillow cases.
The main benefit from using a silk pillow case is that it does not draw moisture out of your skin and hair the way cotton does. Which means less frizzy hair and moisture left in your skin while sleeping. Also silk pillow cases are hypoallergenic. Since silk pillow cases are smooth they do not bundle up like cotton will, so less wrinkles and creases on the face. Silk does not retain body heat, so the pillow has a nice cool feel all through out the night, and helps with a better nights sleep.
Silk pillow cases will run between $18-$25 per single case. It is an investment, but silk pillow cases hold up well with regular washes. The only down side might be that silk pillow cases do not come in a wide variety of colors, so it might not match your sheets and covers. For some it might bother them, but hopefully not!
I found mine on Amazon, they have a great selection.