That's an odd size.
Fabric needed to make a case for standard sized pillows:
12" pillow - 12"x28"
14" pillow - 14"x32"
15" pillow - 15"x24"
16" pillow - 16"x36"
18" pillow - 18"x40"
It's probably too late to help you, but thought you could tweak the 15" pillow measurement to fit your 16x22 size. And if your fleece is a little stretchy, be sure the stretch is running along the width of the pillow, not the length, or it will grow.