First, I have a super-negative mother, too. She can find something to complain about in ANY situation, no matter how great. I don't talk to her any more, haven't for years now, and it did wonders for my mental and emotional health (I'm not saying you need to completely cut your mother off, but I am saying that getting out of the direct "line of fire" of perpetual negativity is very healing and yields positive changes.)
Secondly, I wanted to tell you that I have an autistic daughter. She's 11 now, so not old enough to move out on her own, but I hope that one day she'll have the means and desire to do so, just as you're doing now. Good on you.
I'm also going to tell you that she is the best little manifester I've ever seen. When she sets her mind on having something, it invariably turns up in her reality, sometimes a lot quicker than I would have expected. At this time, her manifestations are mostly things like specific toys or books, but I don't doubt she could manifest anything she wanted (oh, if only I could make her understand what the lottery is...
One thing autistic people are really good at is tuning out stuff you're not interested in. Do that with your mother's negative talk, and focus, instead, on what you DO want. Use that natural tendency to your advantage. You don't have to tell your mother you're not listening to her, you can just nod and say, "Okay," or something like that, while in your own mind, you know what you're REALLY thinking and bringing into your reality. Her negative talk is her own, you don't have to own it, too.
You can certainly manifest anything you want. Your mother probably means well, but misery does love company, and she's probably pretty miserable. (And the parents of autistic kids can be kind of weird about what they think their kids can and can't do; it just goes with the territory, unfortunately.) I think moving away from your mother is a great idea, and I don't think there's any reason why you can't manifest the means to do that AND manifest a girlfriend for yourself, and, hey, anything else you want. There are plenty of autistic people who have great success in life, including a happy relationship.