First off, welcome to HW.
I am so sorry to hear your mother died. She sounds like she was a really wonderful parent.
I tend to agree with Navy about writing a letter, or maybe having a conversation with some of the people at the party. I'm not at all saying you are an alcoholic, but AA does have a pretty good way of handling the negative aftermath of drinking too much (or, as I discovered personally, for any number of negative choices that caused me to bring pain to others). In a nutshell, they are: 1) admit to yourself & your Higher Power exactly what you did wrong, 2) ask Him to remove your shortcomings, 3) make a list of people you harmed & make amends with them, except when doing so would harm them, 4) continue to pray that your Higher Power would keep that from happening again.
Guilt is such a tricky thing. It can motivate us to make things better & move forward, or it can paralyze us and keep us in the past. You've tried to just move on & that hasn't worked, so that is why I thought maybe it might help if instead you tried to make things right -- right with yourself, right with God & right with your family members. If it starts to feel like punishment, then you're not doing it right. It should feel like restoration -- getting back to where you were spiritually/emotionally/relationally before the party. And once you're there, forgive yourself & don't look back. People probably do understand that you were upset & had too much to drink and that's why you said those hurtful things. Once you get past the guilt, I would gently suggest that perhaps you might consider seeing a counselor or joining a grief support group. It sounds like you still carry a lot of pain, which is completely understandable. I think you had the right idea thinking that talking about things would help. It's just that the holiday party may not have been the best place to share all those painful emotions. Maybe having an outlet for that grief & pain on a more regular basis would keep you from boiling over at social events.