Green’s Dictionary of Slang

bottled up adj.

[SE bottled up, contained in a bottle]

fully occupied, unable to take on any new commitments.

[US]A.J. Pollock Und. Speaks 12/1: Bottled up, a proposition that is as good as closed.
[UK]A. Buckeridge Jennings’ Diary 241: Are you feeling excited? I am, sir! [...] All sort of bottled-up with what-d’you-call-it.