My relationship with my dad's gf is really suffering right now because of something I did the other day, and I don't know how to make it up and repair the relationship.

Basically what happened was that we got into a huge fight over something that should have been a small thing.

She accused me of not doing something I disticntly remembered doing, and then I later brought it up to her and accused her lying and messing with me. I basically called her a lying, manipulative POS without bothering to question my memory of things. She said I was the lying one and it basically turned into us shouting at each other and accusing the other person of lying. I never, ever get angry or shout at people so I'm honestly confused as to why I let my feelings boil over like that.

The next day, I am home alone while she's at work. I am feeling bad about it all still but I am calmer and more rational. I realize out of the blue- my memory of doing what it was, was a memory not from yesterday but the day before. I was literally the one who was wrong and saying things that weren't true. On top of that, I just accused someone who I love and loves me, who is one of the nicest most positive people who has been in my life, of doing a nasty manipulative thing that they would never do, and I hurt them deeply. Something was blocking my ability to think rationally or question my own perception and memory of things and I let the thoughts fester in me.

It's three days later now, and I've apologized to her. We're on a little better terms but she's still mad and upset at me. I feel so guilty about having hurt her and accused her of something she would never do. She doesn't trust me and she's really upset with me.

I want to try and make it up to her and be a better person to her going forward, but I don't know how to do that, or if she would wonder if I was even being sincere.

What are some things I could do to better the relationship, or show her I'm sorry and try to heal our relationship?