Green’s Dictionary of Slang

wobbly n.2

also wobbler

[1930s+] a fit of nerves, of panic, of bad temper; thus one who has such attacks.

In phrases

chuck a wobbly (v.)

1. [1980s+] of people, to panic, to suffer a fit of nerves; also used fig. of things.

2. [1960s+] (Aus./N.Z.) to tell a dubious story.

throw a wobbly (v.) (also throw a wobbler)

[1970s+] of people, to panic, to suffer a fit of nerves; also used fig. of things.