Green’s Dictionary of Slang

1. showily or flashily overdressed.

1944		Sun (Sydney) 3 Dec. 7/5: [advert] These styles were created especially for you larger sizes ... not tizzy, and not too matronly - a perfect happy medium!
1949		Argus (Melbourne) 20 Aug. 9/1: The best sellers in a display are as often as not the tizziest.
1953		Baker Aus. Speaks.
1954		Western Mail (Perth) 2 Dec. 27/5: French flowers would be suitable but they are too expensive, while cheap artificial flowers look tizzy.

2. of a person, ostentatious, showy, vulgar.

1984

Partridge DSUE (8th edn) 1241/1: since ca. 1945.

3. of an object, flashy but cheaply manufactured.

1969

G. Johnston Clean Straw for Nothing (1971) 20: I was also going to say I send you lots of presents. Nice things, too. Nothing tizzy [AND].