I [18TM] got blackout drunk with my two friends both [18F] and accidently made one of them really uncomfortable. How do i go about showing I'm truly sorry and apologizing properly?

I wasn't able to post this on r/ relationshipadvice since i'm using a new acc bc I've never touched reddit, so I'm just going to post here hoping to get some much needed advice.

I want to try keep this kind of brief since i don't want my friends finding this, since I've never used reddit and they don't either hopefully they wont. So i turned 18 this year, so did both of my friends, i'll name the first girl toothpaste and the second girl pancake. None of us have ever really had much experience with drinking before, i have gotten slightly tipsy once or twice, but never properly drunk before, this is the same case with pancake, I'm unsure with toothpastes drinking history. (the legal drinking age of where i am is 18).

This all started with the three of us planning a hangout at my house. The day of Toothpaste said she wasn't able to come, so Pancake offered to bring some drinks (vodka) over and just chat since we couldn't do are initial plans without toothpaste. We started drinking around mid day, and in the late afternoon Toothpaste called us and said she would be able to come over, so of course we said yes. By the time she arrived me and Pancake were VERY drunk. I was stumbling everywhere and couldn't stand up properly at all.

We bought more vodka and by this point we were drinking it out of the bottle, Toothpaste started asking why the three of us weren't a couple, both me and pancake rightfully assuming she was joking (since i am a gay trans man, and pancake is still questioning their sexuality. Also she had questioned this before in the past, we also assumed she was joking then) we played along with it. It then became playful kissing on the lips, i thought this was okay, since in the past none of us have been shy of showing physical affection like cuddling, kissing hands, face, cheek.

To me and also Pancake it was all in good fun and I've always been physically affectionate with friends who reciprocate it. By that point i was blacking out drunk, apparently i asked for a threesome from both of them, and called toothpaste "sexy" which i want to say for my sake i was joking, since we have made similar jokes before. But i can't be sure i sounded like i was joking. I wasn't aware i even said it until the next day. I was told Toothpaste left later that night and i was put to bed shortly after, pancake slept over that night and left shortly the next morning.

Today i got a message from toothpaste, she explained to me what i had done and said i had made her uncomfortable and that she didn't really want me being her friend anymore. I feel so awful, my intentions were never to make her uncomfortable and upset, i want to excuse it on being drunk but i know that's still not okay. I know what i did was so wrong, but I'm finding it really hard on figuring out what to say to show i am truly sorry. I don't want to loose her as a friend, but how can i be sure i don't act the same if i get drunk again? Advice would be amazing, if i worded anything wrong or wasn't clear enough please lmk and i can try be more clear.