It is possible you're allergic to the dust mites in you pillow or you may be photosensitive first thing in the morning. Both my daughter and her father sneeze like this first thing.

dust mites

I doubt you're allergic to your actual pillow. More likely you're allergic to the dust mites that survive and breed in your pillow, mattress, boxspring, blanket, and sheets. The highest concentration of these creatures is found in the bedroom, and if you sleep 6 to 8 hours a night....you are sleeping with them! They are microscopic creatures, closely associated to spiders. They survive off of shed human skin. They do not bite you. They have a protein in their feces and difficult body shell (carapace) that a lot people's immune system misidentifies as something else (like a bacteria or virus). As you move about on the bed, a cloud of these microscopic bits goes up in the air and you inhale them. The body misidentifies them and starts a chain reaction that we call an allergic reaction and you call a pain in the butt because you sneeze and sneeze and sneeze. Gross right? But there is help. You obtain these special allergy bedding covers for your mattress and pillow and you wash your sheets every 7 days in the de-mite stuff.

I have terrible dust mite allergy, but when I do these things my allergies are completely under control. I will include a link for how to create a dust free room and a link for the de-mite stuff. So taking just a few steps can stop an dreadful lot of sneezing. Good Luck!