As you already probably know, an ASD diagnosis is only a label. What matters is what you do with it. And as you also probably already know, there are many especially creative, intelligent, and successful people on the Autism Spectrum.
So the answer to your question is — of course you can help yourself. You can learn to manage you emotions and to contain your tendency to rock and flap when in public. You can train yourself to look people in the eye more often. And you can find ways to manage stressful environments. Most important, you can find ways to use your unique strengths and talents and develop your special areas of interest. Fortunately, there are lots of tools available on the Internet.
I’m very sorry your parents aren’t interested in getting an evaluation. It wouldn’t hurt you. If you understood the degree to which you are on the spectrum, you might be able to access some services like special counseling or classes that would help you play to your strengths and work on the issues that get you so upset. If your school has a counselor, you might want to talk to her or him about what kinds of supports might be available to you at school. Your counselor might also help you talk with your parents.
I wish you well.