No. There is nothing wrong with you. There are quite a few people uninterested in sex and relationships. I am one of them.
Your mom sounds like kind of a *****, though. In a way that she actually seems like that instead of embellished to look so by the speaker. If you have trouble making friends, it might be because she is so overbearing.
I think I read another post you made on The Escapist somewhere that mentioned how poorly she takes to things like criticism and, you know, you standing up to her. I seriously reckon you need to escape. Just moving away isn't enough, you have to break yourself away from her emotionally and let her know she can't keep you under her thumb.
It's swell that you want to work for charity and all, but cutting yourself off from your entire family just because one member is a complete dick is not good for you. You will need to face the shitstorm of telling her to go fuck herself. It will be hard, but it is better for both you and her in the long run.
You will make friends. Just the fact that you want to work in charity shows you are a good person. Hell, I'd be friends with you.
And, by the way, physical appearance is not important. Very few people are okay with how they look. You could be gorgeous for all you know, but all you can see is all the tiny little flaws that nobody else pays attention to.
And even that aside, you've seen plenty of people deemed "unnattractive" by shallow fucking idiots in relationships all the time, have you not? Women and men in their fourties who are not exactly going to be appearing on the cover of whatever stupid fashion rag people read these days. They've got age AND mindless societal perceptions against them, but they still manage to find people they connect with.
ANYWAY, what I am saying here is... something I forgot.
HERE I MADE YOU THIS DRUNKEN POST I HOPE YOU LIKE IT