Collocations for pillow - noun

down, feather
satin, silk, velvet, etc. (all esp. AmE)
fluffy, soft
lumpy
throw (AmE) (scatter cushion in BrE)

fluff, fluff up, plump, plump up, punch
She plumped up the pillows for her daughter.

fall back against/on, lie back against/on, sink back against/on
He lay back on his pillows and closed his eyes.

be propped (up) on
bury your face in, bury your head in
She buried her head in the pillow and wept.

case, slip (usually pillowcase, pillowslip)
fight