TIFU by probably outing a colleague

First ever post to Reddit and I've gone anonymous because I'm ashamed.

This happened three days ago, at a work party.

I (31 Male) was drunk, but alcohol isn't an excuse.

I had attended a work party, which by midnight, I, and the majority of the group I was with, where very drunk and walking or stumbling back to a pickup point to our arranged rides home. A gentleman (A) from a different department and team from me, approached and asked me to call my direct colleague (B), as he was sharing a ride home. I dialled the number and just gave him my phone.

B called back and I answered, drunk and started trying to figure out why he'd called, when B said "I don't want you, I want... Oh I can't remember his name" to which I said "Oh, the Gay Guy"

Someone in our group said "The gay guy?" A laughed and said "Yes, I'm gay" and I gave him my phone again to speak to B.

I woke up the next day and felt awful. Firstly I reduced his identity down to his sexuality, secondly I may have even outed him. I can't imagine how he must feel, but I feel awful.

I don't know the dude, he seemed like a good guy, I'm gutted that I've probably upset him.

I've spent the last 3 hours writing an email to HR trying to not sound self deprecating but genuinely apologetic and accepting of the consequences. I couldn't sleep last night, and actually cried relaying the story to my sister.

What am I going to do?

TL;DR I was drunk and made an assumption that a colleague was gay and possibly outed him and used that as my only identification of him.

I'm sorry dude. I'm not that person and I'm gonna try and make it right.

Edit Spelling