Newsflash… Person in early twenties gets too drunk… Pope shits in woods… etc. I don’t think it’s time for an emergency visit to the rehab clinic. When you’re young, you do things to excess, which with the benefit of age and hindsight were really stupid. As you get older, your experience increases, the hangovers get worse and you tend to stop before you go too far.*
I’m no expert in relationships, but I would suggest you don’t immediately break up. I imagine that your girlfriend is feeling absolutely terrible right now, and it’s obvious that you are too. She did something stupid, and then was scared to tell you (because you mean a lot to her), and then kept not telling you, and the longer she left it, the harder it was to tell you, and now you find out in this situation and she will feel she doesn’t deserve you.
Getting through this together could make your relationship stronger - you will know that despite her failings, you love her anyway. I know couples where one partner has strayed, but they have stuck together and are now happily married and very much in love. Remember, she’s younger than you and a certain amount of “am I ready for this commitment?” is to be expected. My girlfriend’s younger than me so it was some time before she was certain we were together for the long haul. It seems your girlfriend had doubts, but is ready for the commitment.
What makes this even more difficult is that it’s a long-distance relationship with you about to make a major step of going to Japan together. Not quite the same as if you were living close to each other, I know. It doesn’t help much, but you need to think about what this girl means to you, could you ever get this from the back of your mind, can you trust her again? Remember, she’s grown up a bit since it happened, and will mature further. Make sure she learns that she needs to talk to you if she gets the feeling she needs to stray.
We can’t do your thinking for you (unfortunately), so this could take some time. Will you regret it if you split up? Correct me if I’m wrong, but I would think that the number of “fish in the sea” is smaller for those looking for same-sex relationships than for straight people. This doesn’t mean you should settle for second best, just that it can take longer to find the one for you. How special is this girl to you?
Don’t rush the decision, and best wishes.
*For the record, I’m only 25 but have been alcohol-free for nearly 4 years following ridiculous problems with alcohol. Quitting is appropriate in some situations - I just don’t think it is in this one.