If you’re unhappy with the size (or cleanliness) of the pillows the airlines provide, consider “making” your own.
Bring an empty, gallon-sized, slide-lock, plastic bag on the plane. After you’ve settled in your seat, close the bag nearly all the way, insert a drinking straw into the opening, and inflate the bag halfway. Then wrap the bag with a sweater or scarf and place this under your head.
On long/international flights, place the tiny pillow provided by the airline in the small of your back rather than under your head. The pillow provides welcome lower back support.