Spanish pillows are long and thin. As wide as the mattress but much thinner than UK pillows. You might be able to get the right size pillow case using Amazon. Most albergues have pillows that have a thin plastic cover that's sealed, as are their mattresses. It does stop bed bug infestation in any pillows or mattresses. Frequently you will be given, or can buy, a disposable paper sheet and pillowcase. I try and use the first one twice so I can carry a set with me in case I stay somewhere without linen available. My quick-dry towel is usually dry by bedtime so I drape that over my pillow, purely for comfort.
I have been bitten by bed bugs, more than once (not just on Camino either), but I very much doubt the pillows are where they hide in albergues, these days. Permethrin doesn't prevent you getting bitten as it takes several hours to kill the bed bugs. There are lots of threads about this! I spray the inside of my pack and the dry bags I use within my pack. I hope that if I pick up a hitch hiker it will die before my next destination.