What should I do if I struggle with same sex attraction (exclusively)? I don't want to live in sin, but I also don't want to spend my life on Earth in loneliness.
I hate to break it to you but even if you were in a relationship, you could (and there will definitely be moments when) be lonely still. Meaningful connections need to be made all the time in our human lives, some of those meaningful connections come from a significant other, but most of them don't. There is a large influence in our culture to only get emotional support, affection, and love from a significant other. But that's not what the human condition is and it's also not what St. Paul advises. When I was discerning religious life asking my priest for guidance he talked to me about how the life of a priest (or any celibate person) is not one of loneliness, there is rarely a moment where someone is not seeking his advice or wisdom or help in something. And he said it's the same in marriage, but that the primary person(s) who are seeking your guidance from is your family, rather than the Church at large. That even in marriage, a married couple, just as they did when they were single, had a duty to their parish to serve as they can. That service may change as they have children, but it is still necessary to have someone who can do those things which the priest cannot oversee. The more you volunteer at your church, the more people you will come into contact with, and form meaningful connections and moments with, and that isn't lonely. Even while in my own relationship, there are moments of loneliness, because I'm working and going through the monotony of life. I'm not alone, but on days when I don't have a meaningful conversation with a coworker or some other person, it bears down on me like a weight.
Romantic relationships don't fight loneliness, they just mask it.
