It's possible you're feeling insecure about your long distance relationship that's bringing doubts about your gf being faithful with you. In order to wrap your brain around it, you opted to do the same in return and let her know about it. Maybe it's your way of saying, "Hey, I'm desirable over here, too!"

You chose a safe mistress to be with.. a willing ex who already knew your sexual style and someone you feel is unattractive. I'm wondering if you're feeling insecure about your sexual performance, too? I suspect this is the part you've omitted from the truth, and maybe because you don't want your gf knowing who the (unattractive) "other woman" is. Maybe you think she'll desire you even more, now that "another woman" wanted you. It's a mind game you might be having with yourself.

I suspect alcohol was just a vice that gave you the excuse to act on an insecurity you're harbouring against your gf.. or the struggles you're dealing with about not knowing who she spends her time with. "It wasn't me. I was drunk! (Who were YOU with?!)"

Long distance relationships are challenging. There's a lot more uncertainty. There's many more reasons/excuses to have an affair. It creates a very insecure and unrealistic way of being. I'd also question if you're still wanting to be in this relationship. Are you purposely (and subconsciously) sabotaging it, as well?

What did your gf say about all this? You didn't mention.

This isn't my opinion, by the way. It's a perception to think about. This is about you understanding where all this is coming from so here's my angle.