late 14c. (implied in crinkled), "become wrinkled or convoluted" (intransitive), from frequentative of Old English crincan, variant of cringan "to bend, yield" (see cringe). Transitive sense of "to form into wrinkles or convolutions" is by 1825. Related: Crinkling. As a noun from 1590s.
"confusedly, hurriedly," 1590s, a "vocal gesture" [OED] probably formed from pig and the animal's suggestions of mess and disorder. Reduplications in the h-/p- pattern are common (as in hanky-panky, hocus-pocus, hinch(y)-pinch(y), an obsolete children's game, attested from c. 1600).
Edward Moor, "Suffolk Words and Phrases" (London, 1823), quotes a list of "conceited rhyming words or reduplications" from the 1768 edition of John Ray's "Collection of English Words Not Generally Used," all said to "signify any confusion or mixture;" the list has higgledy-piggledy, hurly-burly, hodge-podge, mingle-mangle, arsy-versy, kim-kam, hub-bub, crawly-mauly, and hab-nab. "To which he might have added," Moor writes, crincum-crankum, crinkle-crankle, flim-flam, fiddle-faddle, gibble-gabble, harum-scarum, helter-skelter, hiccup-suickup, hocus-pocus, hotch-potch, hugger-mugger, humdrum, hum-strum, hurry-scurry, jibber-jabber, prittle-prattle, shilly-shally, tittle-tattle, and topsy-turvy. Many of these date to the 16th century.