You are not a freak at all. I'm 56 and I'm also single. I've had relationships, but I never felt the need to marry any of them. In fact men in general really bug me because most of the ones I've been involved with have been egotistical, self involved and boring. Obviously I just didn't meet the right one, and that doesn't bother me at all.
I have also never had any maternal urges to reproduce, and I have two cats, so I guess I'm the stereotypical "old scary spinster cat lady", but I certainly don't feel like that. In fact it annoys me that women with cats get that tag, yet women with dogs don't. I would say having cats allows you to be far more independent and outgoing than having dogs, because that's what cats are like and dogs just create work and responsibility that just ties you down.
I would say I've probably had a fuller life than a lot of married women with children/grandchildren because I've had the freedom to do lots of other things they haven't. I retired earlier this year, and after getting through that initial "what the hell am I going to do with the rest of my life" I am now very happy and busy. In fact I have started using that really annoying phrase "I don't know how I had time to go to work". I don't have any family to speak of (both parents are deceased and my brother and I aren't close). Most of my friends are also single (either by choice, or through divorce etc). Some have children and some don't. TBH I try to avoid the ones who are obsessed with talking about their children/grandchildren because the conversation always revolves around them, but most of my friends with children aren't like that and we have a lot of other things in common.
I totally understand that feeling like your life has totally changed. I have always been a strong independent person too, and I also went through a period when meno hit where I thought my whole life was falling apart. In fact it got so bad I actually considered suicide, although I honestly doubt I would have had the guts to do it.
Why don't you give HRT a try? You don't have to keep taking it if you don't want to, but it might make a difference to some of the things you are feeling. I don't think of HRT as "medication". I think of it as a supplement, much like Vitamin D or any other kind of supplement we may take to make out lives healthier or happier.
One final thing, if you are unhappy with some other areas of your life (no friends etc) only you can change that. Try joining some clubs or check out your local area to see if there are some coffee or social groups you can join. Try googling "Meetup.com". You may be surprised by the number of groups around your area. To make friends you have to be the one to make the first move.