Green’s Dictionary of Slang

a strait-laced or jealous person.

1884		(con. c.1840) ‘Mark Twain’ Huckleberry Finn 199: Henry the Eight [...] He was a blossom. He used to marry a new wife every day, and chop off her head next morning.
1887		Bulletin (Sydney) 22 Oct. 8/4: [A]s the Government candidate was sitting peacefully in his office thinking over things, a big, excited man came in with a stick behind him, and asked him if he was the blossom running this show as the friend of the working man?
1905		A. Binstead Mop Fair 35: Her ‘boy’ was a bit of a blossom in some matters.
1948		R. Park Harp in South 97: ‘You’d better watch your step, blossom. Phyllis and Flo are after yer’.