Its all okay if this is a time for you to review how life, media, peers, and your frail ego have convinced you that you need things, girlfriends, fun, alcohol, etc.
Alcohol is a depressant yet aggravated assault on the mind and world first in unleashing the ego to relax, then go too far, then sad. Your fight was not stupid it was part and parcel of being out of harmony with nature which is oh so easy to do, and now you have to contend with being seen as an aggressive offender.
Getting a therapist is great but you'll want to set regular appointments and get cards showing those times. Find free anger management classes and start even if you don't feel like it, because the court system is going to be very strict with you.
If this was an isolated instance you're going to want to show up in court with every piece of paper you can that shows proactive action self motivated.
You should probably watch what you say as well and keep statements simple and to the point without sounding like a martyr.
Verbal fights can escalate, but society fears males that strike females. Females can strike males and get away with it a lot but not always, but damn sure white knights will protect females in concept with vigor.
No not drink period. Do not email or text anyone about this. Address what's I'm your life that's working well, ask for help and do research but know you've got to have this be the final time you react with violence and actually find way to forgive yourself while understanding it. Do not focus on the gf or try repair as you will follow a pattern that often fails and that order is serious against you. The prosecution may want stiff penalties but judge may not. See therapy and anger mgmt courses as necessary even if it feels contrived and ass covering.
Once some time has passed you will be informed and see that the worst has happened if you're humble. Right now you're in grave danger of pity drinking, wallowing and over thinking, and contact of any kind with her or her family will be a horrible idea due to legal system.
When you appear with therapy and anger mgmt already engaged, you will see the court in end wants you to self manage yourself.
Read self help books vs media, internet crap, and tangents that show off ego this, desire that, etc etc.
See this as a blessing to get at core of your actual role in life and how much work it is just trying to avoid negative shallow ego based crap surrounding us. You need to love all and yourself before relationship with others and don't pretend the fight was over nothing. It was two intoxicated people trying to keep up with a Facebook ego world screaming at you you must be happy , can just go party without consequence and booze is great, and relationships and sex are entitled things everyone needs.
Maybe you're a swell guy or maybe you're a lying asshole, who cares, you found a way to get to core and be grateful to be alive and healthy and an apex predator in a species that must find a way asap to reverse the consumption and rampant ego dance or the entire planet and all life on it will die. You could be in one year from now seeing things very differently and helping others. Use the shame but don't get lost in it.
If you can get away from humans and be in quiet nature any do so. Respect the whole history of life and see how much suffering has also been wonderfully offset by care and respect. Get calm and quiet and work out slowly from there. Avoid telling your story much and just be an active observer in anger management sessions. They're free and everywhere so no excuses. If you can't find one, demand therapist helps you find one, and know not all therapists are perfect fits. Talk to current one if you feel like leaving him/her and why if so.
Mediation should not be this phone app guided bullshit of over thought, just practice being still so you don't get as inflamed in future.
Prove you're a good man by actions of outside help, self help, humility, and discovery of others who found selves in same position.
If you secretly know you actually have a substance issue, address it. If you don't , don't pawn of striking her in anger on the booze. Own it, and move forward.
That's one input perspective.