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I don't think it's a good idea that you tell your boyfriend if you don't know what happened even though you stayed the night, you aren't sure what happened so why make a mountain out of a molehill until you actually know what you did with the ex you already told him that you kissed him and he is willing to work at it, then work on that and make sure that you cut off all contact with the ex that is important in order for you and your current boyfriend to work through this and if you truly want to forgive yourself then you have to get rid of all of the things that make you vulnerable, the alcohol and the ex and concentrate on your relationship with your boyfriend. Long distance relationships are very hard especially when you don't see each other much so what you have to do is realize that you are only human and will make many more mistakes along the way as long as you acknowledge that you made the mistake and work towards not making that mistake again.
Some of the biggest challenges you will face in your long distance relationship are, Communication, Closeness and Trust. Many relationships suffer from these 3 challenges, what makes your relationship even more challenging is the distance factor, you get lonely for your boyfriend and the feeling of closeness and yearn to have someone close to you and this could be part of the reason you made this mistake but as long as you are willing to correct it then you shouldn't feel guilty you told your boyfriend what you actually knew and remembered doing. When you are around someone everyday you have the body language along with conversation. You have the touch when you are sad or alone. You have a sense of trust because they are close by. With long distance relationships you must now rely on a new senses and styles to effectively keep these together and trust your mate. I wouldn't beat yourself up until you remember what you actually did then you told him what you knew.