I'm sorry you're going through this. Anxiety is so difficult to live with.
What do you think is the worst that would happen if you went with your fiancé one Saturday night? Or if you made a commitment to yourself and/or to him that you would make the effort to go once a month? That might help you, both in your relationship and in your anxiety. Also, are there other things you can do on a Saturday night? Or any other night for that matter? Anything you can do socially that will make you feel less excluded as a result of your anxiety?
I, too, struggle with making comparisons of myself against others, and it directly affects my anxiety. I have social anxiety as it is, and I go through periods of months without seeing my friends, or really leaving my house at all if I don't absolutely have to. Those are always the times when I judge myself most. But I have a sister who is a super woman. She has two young, hyper kids, a dog, and a husband who doesn't do much at all to help out, but somehow her house is always spotless, every meal she serves (and she serves every meal without fail) is five-star gourmet, she does all her own shopping, takes the kids to and from school, she makes cakes professionally, she knits, cans food, paints, and now on top of it all she's a fitness instructor and personal trainer, and does all of this extremely well, and manages to have a social life on top of it. Just thinking about it right now exhausts me, lol. But when I look closer I know that the reason she does so much all the time is because she literally cannot sit till. That's how she deals with her own anxiety - she has ADHD. Yes, she is good at these things. And yes, it's really intimidating, and hard not to compare myself to her and come up short. But all I have to do is visit her and I remember how uncomfortable I feel in her house. She never has the time to take five minutes to sit with me and visit. She is always shouting from the other room in our conversations because she is cooking, or mopping a floor, or making a list, or helping one of the kids with something. I can't imagine living like that. It's not the kind of life I want for myself.
I guess what I'm getting at is, it is always easy enough to look at someone else's life and make assumptions about how much they do or don't have, how well the do things, what they have or lack, etc. And chances are there's always going to be someone else judging me in the same way. But I only have to make my life work for me. I have my wife, my school, and my own house. I have my friends, my art, my writing. I have things in my life that are important to me and those are the things that I try to focus on, because when I start thinking about the things other people have or do, and whether or not they like me, I can drive myself crazy with that stuff, especially with my panic and anxiety disorders.
So. *whew* Sorry, didn't mean this to be such a long response. I guess what my advice would be - and please, take what you like and leave the rest - is that you should do what feels right for you. In saying that, don't avoid things just because you think they might be uncomfortable, but don't always push yourself to go because you think you "should", either. Try to strike a balance. Engage in things once in awhile that your fiancé enjoys, and in the meantime, find other things to do that you truly enjoy as well, with people you feel comfortable with and who accept you for who you are, because that will make you feel a lot stronger in other social situations. It's so important to be accepted for who we are in some area of our lives.
Good luck with everything...