I (30M) lost my cool, gf (25F) is deeply upset, how do I heal this?

To set the scene: I came home to my cluttered apartment after a 9+hr shift, underfed & overheated & exhausted, feeling unprepared for a heavier discussion planned for the night with my gf about our relationship. She & I both suffered bad days, and our brief interactions on the phone were tense as she was short with me, so when I came home I fully admit I felt defensive and irritated. I perceived myself as leaving one kind of hard work for another, with no chance for respite.

According to her, I gave her an odd look, distracting to the point that when she walked in my apt and I went in for a hug, she claims she forgot she didn’t hug me back. In hindsight I see it as purely tired miscommunication, but in the moment I saw myself as trying show affection despite my irritation & being rebuffed. I perceived her as being ready for conflict. Add into the mix my dread about our planned conversation as well as raw grief over a deceased pet in my family, and before I knew it we were in an argument.

In full objectivity, I was the one who escalated our conflict, more reactive and forgetting to walk away & breathe. I confronted her about the way she’d been talking to me during the day and it spun out of control from there, as she quickly grew defensive & we both grew upset. I’m a louder person especially when emotional; she perceived my raised tones as me screaming at her & the situation crumbled even further, to the point of tears on her end.

So then my biggest mistake & truest regret, reacting without thinking, was to blurt out “You’re fucking crying? I should be crying after the day I had”, which upset her to the point of threatening to walk out. I told her to go then if she wanted to, and she did, driving away for about 10-20 min before coming back of her own accord. In the meanwhile I cooled down & realized I’d not been my best self, intending to give her space to heal until we could talk. Our conversation after she came back wasn’t productive, to say the least. Three hours of hard feelings, stunned silence, and unhappiness on both ends, with my apologies unaccepted.

We’ve only had one other instance before where I lashed out from frustration. I refuse to be insulting in the sense of calling people names in anger, so the last time we had this kind of fight, she was deeply upset because I told her to act like a grown woman & handle her emotions, which is another regret of mine. Another part of the problem is that my gf told me after this previous fight the next one would make her leave me & our relationship. She made me promise this would never happen again, and now that it has, our relationship is looking grim. She’s deeply hurt even now by this second most recent fight, not texting me and reluctant to spend time together in the coming days.

I know I messed up. I know I wasn’t my best self, wasn’t taking the time to breathe & de-escalate. If more context is needed, I can provide; I just want to know, how can I heal this hurt?

TLDR: lost my temper during an argument & gf is deeply hurt & ready to leave, how do I heal this pain?