In my experience there are two types of parents when it comes to AS - those who go all out with it, decide to tell everyone else you have it, diagnose everyone else with it, and just generally try TOO hard. Then you have those who either don't believe/accept that you have it or just try not to talk about it, or like you talking about it. This is usually because they believe their kid having a label could get them teased, bullied, etc, and they want their child to be -normal-. EVERYONE wants their children to be normal, and I'm sure (though I don't know anything about your family at all so I apologise if I'm completely wrong) that they only feel that way because they are either afraid of what having a diagnosis means, that it could mean you get treated differently etc, or because they think you're just trying to find an excuse for the way you are, or that you are just being a hypochondriac. Parents can sometimes be quick to assume their teenagers (I'm assuming that's what you are) are naturally wrong in their opinions simply because they are teenagers, unfortunately, and take their kids opinions less seriously. Could you perhaps print off a simple fact sheet about what Aspergers actually is (I'm sure there are plenty on the net) and show it to them? If they see those symptons laid out in front of them it might click in their head and realise what you're saying may be true.
In either case, having a diagnosis will definitely help, and at the end of the day, being your parents, I am sure if it was made clear to them that you do have AS (If you truly do) then they will be supportive. Just try and be clear and logical about why you think you do have Aspergers, and if at teh end of the day they still aren't willing to listen, then it isn't the end of the world, because there are plenty of people out there who can give you support - just make sure that no matter what they respect you, and even if they disagree with you about having AS, that they can't "make fun" of you, because it's their job to support and encourage you, and if what they are doing is making you feel bad and even worse, then they shouldn't be doing it. If you had a chat with them, let them knew just how much of an effect it was having on you I'm sure they'd try their best to change.