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Middle English prikke, from Old English prica (n.) "point, puncture; particle, small portion of space or time," common West Germanic (cf. Low German prik "point," Middle Dutch prick, Dutch prik, Swedish prick "point, dot"). Meaning "pointed weapon, dagger" is first attested 1550s.
Earliest recorded use for "penis" is 1590s (Shakespeare puns upon it). My prick was used 16c.-17c. as a term of endearment by "immodest maids" for their boyfriends. As a term of abuse, it is attested by 1929. Prick-teaser attested from 1958. To kick against the pricks (Acts ix:5, first in the translation of 1382) is probably from sense of "a goad for oxen" (mid-14c.).
Old English prician "to prick, pierce, prick out, sting," from West Germanic *prikojanan (cf. Low German pricken, Dutch prikken "to prick"); Danish prikke "to mark with dots," Swedish pricka "to point, prick, mark with dots" probably are from Low German. Related: Pricked; pricking. To prick up one's ears is 1580s, originally of animals with pointed ears (prycke-eared, of foxes, is from 1520s).