Green’s Dictionary of Slang

ill-tempered, obsessed with irrelevancies and petty problems.

1959		Galton & Simpson ‘Hancock in Hospital’ Hancock’s Half-Hour [radio script] I’m sorry I was a bit niggly.
1960		G.W. Target Teachers (1962) 260: She read it a bit niggly.
1971		F.J. Hardy Outcasts of Foolgarah (1975) 82: He suffers from an acid stomach, and that makes him niggly.
1980		J. McClure Spike Island (1981) 325: Very few policemen realise that the reason they’re a bit niggly the week before [...] has any association with that [i.e. menstruation].