Dictionaries of British slang are awash in piss terms, but most of them don't mention verb forms that combine piss and up. Consistent with the Oxford Dictionaries definition of "piss something up" cited in the answer given by "Keep these mind", John Ayto & John Simpson, The Oxford Dictionary of Modern Slang (1992) has this entry for to piss up:
to piss up to spoil or ruin Cf. PISS-UP noun 1 ["A mess-up; a bungle or confusion"] 1937–.
Ayto & Simpson reports that the noun form of piss-up is younger than the verb form of to piss up, dating only to 1950, but that it is nevertheless two years older than the more widely recognized modern meaning of piss-up as a noun ("a bout of heavy drinking," according to this dictionary; "a drunken party," according to Jonathon Green, The Dictionary of Contemporary Slang [1984]).
Jonathon Green, Chambers Slang Dictionary (2008) provides three meanings for the verb phrase piss up, none of them very similar to Ayto & Simpson's definition:
piss up v. 1 {1960s–1970s} (U.S.) to vomit 2 see PISS OFF v. (2) ["to annoy"]. 3 see PISS ON v ["to treat contemptuously"].
More to the present point, Green has entries specifically for piss it up and for piss it up the wall:
piss it up v {fig. use of sense 2 ["to urinate"] above} {1960s+} to drink. piss it up the wall {var. on next [piss (money) against the wall)]} {late 15C+} to waste money on drink; thus to waste money in general.
Green also lists these "pissing up" phrases: piss up a rope ("to be engaged in a futile exercise"—U.S. slang), piss up someone's back ("to flatter someone"), piss up someone's leg ("to lie, to deceive"— U.S. slang), and piss up a storm ("to complain strongly, to make a major fuss"—U.S. slang).
Tony Thorne, The Dictionary of Contemporary Slang (1990) has an interesting note on the noun piss-up:
piss-up n British a drinking bout, drunken celebration. A vulgarism used neutrally or with cheerful overtones rather than disapprovingly.
I think that Green's definition of piss it up ("to drink") is the one relevant to the poster's question:
I was with my girlfriend at the time, and I was out [drinking] too much, really, and was pretty horrible to her, frankly.
Green says that the phrase goes back to the 1970s and involves a figurative use of piss in the sense of "to urinate." It might be slightly more accurate to say that the phrase alludes to a necessary physiological consequence of heavy drinking.
