I'm in high school, and I am asexual. It took me a little while to figure that out, especially since I don't know anyone else who is openly asexual. In fact, I'm still kind of figuring everything out. Anyway, my parents are total liberal progressive people in general, and they have plenty of non-straight friends, so I thought when I came out to my mom she would be cool about it. Well, no. She FREAKED OUT and is all convinced I was sexually abused (I wasn't) and is trying to force me to see a psychiatrist. Obviously, I wish I hadn't told her, but what should I do? I still have a year and a half before I graduate and I'd rather not spend it trying to convince my mom to relax.
Oh man, parents are never happy. They flip their shit when you tell them you're having sex, and they flip their shit when you tell them you're not interested in having sex. She should just be glad you're not sexting all over town (because why does everyone have their panties in a twist about teens sexting? You know how you cannot get pregnant/an STD? Through a cell phone!).
Anyway, I don't mean to make light of your situation. It sucks sucks sucks to have your parents not be supportive of your orientation, especially since now is probably a time when you could use somebody to talk to about shit and whatever. I think it's awesome, though, that you felt comfortable enough with yourself and them that you could be open, even though it didn't happen like you'd hoped it would.
The thing is just that your mom is probably not very well educated about asexuality—as you say, a lot of people don't know any out asexual people. When she calms down a little, maybe send her to the FAQ at asexuality.org. Hopefully you've checked them out already, as they have a bunch of really useful information and also a forum where you can talk to other people who are going through/have gone through the same stuff you are.
I know that you are probably hurt and pissed, but I would say cut her a little slack. A lot of people find out that however "progressive" they think they are, there's an unexamined assumption of status-quo normativity when it comes to their kids, and they react poorly when that assumption is wrong. Again, it's shitty, but not having a relationship with your mom would be even shittier.
So, I would suggest that after you've both (but especially she) had time to calm down, and maybe after you've sent her some stuff to read, broach the subject again. Explain that no, you haven't been sexually abused, that this is just how you are and it is a normal way for people to be, etc. I would hope this would be enough to convince her to trust you and accept what you are saying.
If she insists on you seeing a psychiatrist, ask if you can help pick the person out. Hopefully you can find someone open-minded who can help you convince her that she is in the wrong. If nothing else, it would be someone you could talk to about what you're going through with your mom.
I'm sorry this shook out the way it did, but I have hope your mom'll come around. Good luck!