Flying across the world to save the relationship

I have been with my boyfriend in a happy (gay) relationship for the last 1 year and 6 months. Now, I actually moved to the US 2 months ago (for 1-2 years with an arrangement that I would see him every 2 months or more often), which was a hard step to do for both of us (he is in Europe now). We were both insanely in love.

Now, I screwed up. I had a random drunk sexual encounter in a gay club (which never happened to me before...) and got a Gonorrhea infection from it. I felt so bad about it, I immediately told him. What makes things worse is that I also lied about the encounter at first and only told him when I was told that I have an infection. After he seemed fine with it just after I told him, he then changed his mind a day later, told me how disgusted he was and broke up with me, saying very strong things: "I don't see a future with you", "It's done and it's done for forever". He usually sticks to things he says, which scares me.

Now I am sitting in the US feeling sorry for myself and for my stupidity - I really loved this person more than anyone before and I wish he could see that. For me, the sexual encounter didn't mean anything, but I know that is a bad excuse. All I know is that I immensely care about him and want to spend my life with him.

I know I screwed up, but we both love each other. I learned my lesson, I'd never do anything like this again. I just want him back at some point.

After we broke up on Saturday, I have been thinking what I should do. After speaking to my friends, I am thinking about going over to Europe and showing up on his doorstep, seeking a face-to-face discussion. This would involve a massive trip, not even knowing if he would open the door.

I am afraid that he won't be willing to talk to me and that he will shut me down. The days since the breakup have been the hardest in my life, I was truly suffering. I would not know what to do when he actually would decide to shut me down completely.

Should I still go? What should I do? I truly care about this person.

Thanks for your help!!

Any advice?