You did exactly the right thing for the following reasons :-
You were at risk if the allegations were untrue or the pilot concerned denied the problem.... it happens.
By reporting to the union and having them handle things initially your union was in a position to consider the legal and welfare issues affecting both you and the offending pilot.
The union is also able to make discrete enquiries to confirm whether a problem really exists or not prior to a possibly genuine but unfounded allegation is made to management.... career damaging stuff for both of you.
The situation would be much harder if you genuinely felt there was a problem and the union refused to deal with it. Under those circumstances you really have no option but to report it to management.
Alcoholism is a sickness... responsible companies have plans jointly agreed with the unions to deal with and manage the sickness for the betterment of all parties.
On the other hand the part time drunk who gets pissed on an overnight, is not an alcoholic and turns up for work under the influence has NO excuse and should be fired on the spot.