Hello there, I'm writing you regarding an...

Hello there, I'm writing you regarding an incident that happened to me very recently, which will be a week ago by tomorrow. I had a girlfriend for one year and 2 months. Our relationship was OK. However, I wouldn't call it excellent, but we were getting on more by time. Until about a month ago, things started going out of hand, we argued a lot, we started thinking about splitting up, which involved many reasons. Not only that we argued, but also the future didn't seem very possible for us as she's a foreign in my country and will probably leave within the next 2 years. And that I might not be able to leave as well at the same time and that this could be the end of us. So, during this last month, we didn't see each other often, neither did we sleep together for the whole month. Here comes the more important part. I've had a crush on that girl, maybe a bit before my girlfriend and I started arguing, and I had the feeling that she liked me, but nothing happened between us until a week ago. I was out with a group of friends, including that girl. When we left the place, I was giving my friends a ride and intended to drop this girl at the last. So, she invited me to her place and things went out of control after few drinks and we ended up having sex! By this point, my girlfriend and I were technically still together, but like I explained earlier, we have not been intimate for a month. Although, I felt very guilty and couldn't stop thinking and Bern awake for most of the nights. Till I decided that I should split up with my girlfriend and took that as a sign that our relationship should end. Which I did last night, my girlfriend also thought that maybe we're not compatible at the moment for many reasons. To which I agreed to, or in other words, I felt like I had to do. My question is, did I actually cheat on my girlfriend given the circumstances that I mentioned earlier? P.S, the girl I slept with is a common friend to me and my girlfriend. I wouldn't call her a close friend to my girlfriend, but we usually all go out together. I need an advise. Thank you for taking the time to read my message.