There's a chance you can get a diagnosis without having to tell your parents, but that decision is unfortunately left up to your doctor after he meets you. He or she will decide after meeting and evaluating you whether or not telling your parents and including them in any treatment plan would be detrimental to your health or wellbeing. If they decide that telling your parents would be bad for you (if you explained why it would be bad to your doctor, he/she might see your point and decide that your parents don't need to be included in your treatment), they don't have to do so. If you feel as though you can't get evaluated without your parents because of cost, it might be harder to avoid what you don't want. In some circumstances, you may be able go to the doctor by yourself if you're really trying to make sure they don't know any possible diagnosis you could receive.

Have you tried to talk to your parents about the way their actions are making you feel? I can imagine that them trying to claim you have autism is frustrating, not because autism is inherently negative, but because your parents treating you differently than expected is maddening. Talking to parents is hard, but if you have reasonable parents who would possible listen to what you say, I would suggest trying it.

I hope things become easier for you soon, good luck with everything.