I wondered this, too. OP, was any money exchanged? Not that it makes much difference to the cheating itself, but it seems a bit odd that apparently within minutes of this woman approaching you, you two were already in bed.
All you can do is be honest with your girlfriend and let the chips fall where they may. Keep getting tested per your doctor's recommendations, as some infections won't show up in your system right away.
You were not using your best judgement, but you were also clear-headed enough to get into bed (and out), and stay upright long enough to get yourself back to your own accommodation. Keep that in mind. Alcohol may have impaired you but you made the choice to cheat all on your own. Something is going on inside you that wanted to sleep with someone else. You need to explore that (with yourself) and figure out what isn't lining up in your story of your romance with your girlfriend.