There are two aspects of it.
One is that you really got so drunk that you were not in your senses.
Another is that you were drunk just enough to let your subconscious prevail over your conscious.
If it’s the first one i think you should seriously tell your boyfriend everything and accept that you did a mistake and that you would never do it in your senses. Not telling him might boost your nasty subconscious and you may be prone to do it in future.

If it’s the second one, then i think introspect yourself. What let you do it. Because at one stage we remember what we are doing and what we did.

There is one more better option. If you can promise yourself that such thing will never happen in future ni matter what then i think you should forget what happened. No need to tell him. You can get over your guilt by being extra caring towards him. This way you can give yourself one more chance to correct yourself without putting him in tension. Or else whether he forgets you or not, next time when he is out he may think that you might do something like that again.
So give yourself one chance if you are sure that you will never ever do it again.

I think facebook is becoming obsolete day by day because of the following reasons –

1.the coming of more interactive applications which enable people to interact in real time.

2.the major data breaches and other allegations on Facebook which have put questions on its data handling capabilities.

3.the wave of de-socialisation seen in todays era.
People, rather than being open to other’s ideas and lifes, are choosing to assert their own views.

In other words from an era of discussion and consultations we are moving towards one way assertion of our own “right” over other’s “wrongs”.
Thus in such an environment Facebook is bound to loose relevance.

It is rather interesting to note that the people’s disinterest in facebook is being accompanied by increasing popularity of Twitter. The trend is easily predictable as on twitter one can write his/her opinion and be seen by thousand others without any formal friend request or risks of privacy.

Thus, the decreasing popularity or interest in facebook can be attributed to both Facebook’s own doing and also the change in our societal structure .